{"id":1120,"date":"2024-12-22T10:23:39","date_gmt":"2024-12-22T10:23:39","guid":{"rendered":"https:\/\/www.mathros.net.ua\/en\/?page_id=1120"},"modified":"2025-09-04T16:09:05","modified_gmt":"2025-09-04T16:09:05","slug":"trapezium-rule-calculator","status":"publish","type":"page","link":"https:\/\/www.mathros.net.ua\/en\/trapezium-rule-calculator","title":{"rendered":"Trapezium Rule Calculator"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1120\" class=\"elementor elementor-1120\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cc1493c e-flex e-con-boxed e-con e-parent\" data-id=\"cc1493c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-066526a elementor-widget elementor-widget-html\" data-id=\"066526a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"h2-title\">Want Your Definite Integral Calculated in a Snap? Use Our Online Calculator for Instant and Easy Results!<\/h2>\n<style>\n    .h2-title {\n        text-align: center; \/* \u0412\u0438\u0440\u0456\u0432\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u043f\u043e \u0446\u0435\u043d\u0442\u0440\u0443 *\/\n        color: gray; \/* \u0417\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0441\u0456\u0440\u043e\u0433\u043e \u043a\u043e\u043b\u044c\u043e\u0440\u0443 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-size: 24px; \/* \u0422\u0440\u043e\u0445\u0438 \u0431\u0456\u043b\u044c\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-weight: 600; \/* \u041d\u0430\u043f\u0456\u0432\u0436\u0438\u0440\u043d\u0438\u0439 \u0448\u0440\u0438\u0444\u0442 \u0434\u043b\u044f \u0430\u043a\u0446\u0435\u043d\u0442\u0443 *\/\n        line-height: 1.4; \/* \u041a\u043e\u043c\u0444\u043e\u0440\u0442\u043d\u0438\u0439 \u043c\u0456\u0436\u0440\u044f\u0434\u043a\u043e\u0432\u0438\u0439 \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b *\/\n        margin-top: 5px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u0437\u0432\u0435\u0440\u0445\u0443 \u0434\u043b\u044f \u0433\u0430\u0440\u043c\u043e\u043d\u0456\u0439\u043d\u043e\u0441\u0442\u0456 *\/\n        margin-bottom: 15px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u0437\u043d\u0438\u0437\u0443 *\/\n        padding: 10px; \/* \u0412\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f \u0434\u043b\u044f \u043a\u0440\u0430\u0449\u043e\u0433\u043e \u0432\u0438\u0433\u043b\u044f\u0434\u0443 *\/\n        font-family: 'Arial', sans-serif; \/* \u0417\u0440\u0443\u0447\u043d\u0438\u0439 \u0456 \u0447\u0438\u0442\u0430\u0431\u0435\u043b\u044c\u043d\u0438\u0439 \u0448\u0440\u0438\u0444\u0442 *\/\n        word-wrap: break-word; \/* \u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0441\u043b\u0456\u0432 \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n    }\n\n    \/* \u0410\u0434\u0430\u043f\u0442\u0430\u0446\u0456\u044f \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n    @media (max-width: 768px) {\n        .h2-title {\n            font-size: 20px; \/* \u0417\u043c\u0435\u043d\u0448\u0435\u043d\u043d\u044f \u0440\u043e\u0437\u043c\u0456\u0440\u0443 \u0442\u0435\u043a\u0441\u0442\u0443 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n            padding: 8px; \/* \u041c\u0435\u043d\u0448\u0438\u0439 \u0432\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n        }\n    }\n\n    @media (max-width: 480px) {\n        .h2-title {\n            font-size: 18px; \/* \u041e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 \u0434\u043b\u044f \u0441\u043c\u0430\u0440\u0442\u0444\u043e\u043d\u0456\u0432 *\/\n            padding: 5px; \/* \u041c\u0456\u043d\u0456\u043c\u0430\u043b\u044c\u043d\u0438\u0439 \u0432\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n        }\n    }\n<\/style>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0c685c4 elementor-widget elementor-widget-html\" data-id=\"0c685c4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<script type=\"text\/javascript\" async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\"><\/script>\n<link rel=\"stylesheet\" href=\"mathquill\/lib\/mathquill.css\">\n<script src=\"mathquill\/lib\/jquery.min.js\"><\/script>\n<script src=\"mathquill\/lib\/mathquill.min.js\"><\/script>\n<script src=\"https:\/\/d3js.org\/d3.v7.min.js\"><\/script> <!-- D3.js library -->\n  \n<div class=\"calculator-container\">\n    <div class=\"equation-container\">\n        <label for=\"inputField\">Integrand Function (e.g., <i>\"x^2\"<\/i>, <i>\"sin(x)\"<\/i>, <i>\"exp(x)\"<\/i>)<\/label>\n        <hr>\n        <div class=\"calcKeypad\">\n            <button class=\"padBtn\" onclick=\"addSymbol('x^n')\">x^n<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\sqrt{}')\">\u221ax<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\cdot')\">\u00b7<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\frac{}{}')\">x\/y<\/button>\n             <button class=\"padBtn\" onclick=\"addSymbol('\\\\exp()')\">exp<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\sin()')\">sin<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\cos()')\">cos<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\tan()')\">tan<\/button>\n            <button class=\"padBtn\" onclick=\"addSymbol('\\\\log()')\">log<\/button>\n        <\/div>\n        <span id=\"inputField\" contenteditable=\"true\" class=\"math-input\"><\/span>\n    <\/div>\n    \n    \n    \n    <div class=\"parameter-container\">\n        <!--<input type=\"text\" id=\"function\" name=\"function\" required \/>-->\n        <label for=\"lower_limit\">Lower Integration Limit<\/label>\n        <input type=\"number\" id=\"lower_limit\" name=\"lower_limit\" required \/>\n        <label for=\"upper_limit\">Upper Integration Limit<\/label>\n        <input type=\"number\" id=\"upper_limit\" name=\"upper_limit\" required \/>\n        <label for=\"num_partitions\">Number of Partitions for the Integration Interval<\/label>\n        <input type=\"number\" id=\"num_partitions\" name=\"num_partitions\" required>\n    <\/div>\n    \n    <input type=\"button\" id=\"generate-button\" name=\"integral\"  value=\"Calculate\" onclick=\"calculateIntegral()\" \/>\n    <div id=\"info-block\" class=\"info-message\">\n        When you <strong>reduce the step size<\/strong> and <strong>increase the number of intervals<\/strong>, your result becomes much more <strong>accurate<\/strong>\u2014try it!.\n    <\/div>\n<\/div>\n<div id=\"calculation-results\" style=\"display: none;\">\n        \n    <div id=\"fcontainer\" class=\"solution-container\"><\/div>\n<\/div>\n<div id=\"error-block\" class=\"error-message\"><\/div>\n<div id=\"loading\" class=\"loader\" style=\"display: none;\"><\/div>\n\n<style>\n    .info-message {\n        background-color: #eaf6ff; \/* \u0421\u0432\u0456\u0442\u043b\u043e-\u0431\u043b\u0430\u043a\u0438\u0442\u043d\u0438\u0439 \u0444\u043e\u043d \u0434\u043b\u044f \u0432\u0438\u0434\u0456\u043b\u0435\u043d\u043d\u044f *\/\n        color: #0b638b; \/* \u0422\u0435\u043c\u043d\u043e-\u0441\u0438\u043d\u0456\u0439 \u0442\u0435\u043a\u0441\u0442 *\/\n        border-left: 4px solid #0b638b; \/* 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\u043c\u0456\u0436\u0440\u044f\u0434\u043a\u043e\u0432\u0438\u0439 \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b *\/\n        text-align: left; \/* \u0412\u0438\u0440\u0456\u0432\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u043f\u043e \u043b\u0456\u0432\u043e\u043c\u0443 \u043a\u0440\u0430\u044e *\/\n    }\n\n\/* \u0417\u0430\u0433\u0430\u043b\u044c\u043d\u0456 \u0441\u0442\u0438\u043b\u0456 \u0434\u043b\u044f \u0441\u0442\u043e\u0440\u0456\u043d\u043a\u0438 *\/\n    body {\n        font-family: 'Arial', sans-serif;\n        margin: 0;\n        padding: 0;\n        background-color: #f4f4f4;\n    }\n    \n    \/* \u041e\u0441\u043d\u043e\u0432\u043d\u0438\u0439 \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u0430 *\/\n    .calculator-container {\n        max-width: 600px;\n        margin: 0 auto;\n        padding: 20px;\n        text-align: center;\n    }\n    \n    \/* \u041a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u0434\u043b\u044f \u0432\u0432\u0435\u0434\u0435\u043d\u043d\u044f \u0440\u0456\u0432\u043d\u044f\u043d\u044c *\/\n    .equation-container {\n        background-color: #0B638B;\n        padding: 20px;\n        border-radius: 8px;\n        margin-bottom: 20px;\n        color: #fff;\n    }\n    \n    \/* \u041a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u0434\u043b\u044f \u0432\u0432\u0435\u0434\u0435\u043d\u043d\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 *\/\n    .parameter-container {\n        background-color: white;\n        padding-left: 20px;\n        padding-right: 20px;\n        border-radius: 8px;\n        margin-bottom: 20px;\n        color: #fff;\n    }\n    \n    \/* \u0421\u0442\u0438\u043b\u044c \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0456\u0432 \u0442\u0430 \u043c\u0456\u0442\u043e\u043a *\/\n    label {\n        display: block;\n        margin-bottom: 8px;\n        font-size: 16px;\n        color: #555;\n        font-weight: 600;\n        text-align: left;\n    }\n    \n    .equation-container label {\n        color: #fff;\n        font-weight: bold;\n    }\n    \n    \/* \u041f\u043e\u043b\u044f \u0434\u043b\u044f \u0432\u0432\u0435\u0434\u0435\u043d\u043d\u044f \u0440\u0456\u0432\u043d\u044f\u043d\u044c *\/\n    .math-input {\n        display: block;\n        width: 100%;\n        min-height: 40px;\n        padding: 10px;\n        border: none;\n        border-radius: 6px;\n        background: #fff;\n        font-size: 16px;\n        text-align: left;\n        color: #333;\n        cursor: text;\n    }\n    \n    \/* \u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430 \u043b\u0456\u043d\u0456\u044f *\/\n    .equation-container hr {\n        border: none;\n        height: 1px;\n        background: linear-gradient(to right, rgba(255, 255, 255, 0.8), rgba(255, 255, 255, 0.2));\n        margin-bottom: 15px;\n    }\n    \n    \/* \u041f\u043e\u043b\u044f \u0432\u0432\u043e\u0434\u0443 \u0442\u0430 \u0432\u0438\u043f\u0430\u0434\u0430\u044e\u0447\u0438\u0439 \u0441\u043f\u0438\u0441\u043e\u043a *\/\n    input, select {\n        width: 100%;\n        padding: 10px;\n        margin: 7px 0;\n        border: 1px solid #ddd;\n        border-radius: 5px;\n        font-size: 16px;\n    }\n    \n    \/* \u041a\u043b\u0430\u0432\u0456\u0430\u0442\u0443\u0440\u0430 \u0437 \u043a\u043d\u043e\u043f\u043a\u0430\u043c\u0438 *\/\n    .calcKeypad {\n        display: flex;\n        flex-wrap: wrap;\n        justify-content: center;\n        gap: 5px;\n        margin: 15px 0;\n    }\n    \n    .padBtn {\n        padding: 10px;\n        background-color: rgba(255, 255, 255, 0.2);\n        color: #fff;\n        border-radius: 5px;\n        font-size: 14px;\n        cursor: pointer;\n        transition: all 0.3s ease;\n        border: none;\n    }\n    \n    .padBtn:hover {\n        background-color: rgba(255, 255, 255, 0.4);\n    }\n    \n    \/* \u041a\u043d\u043e\u043f\u043a\u0430 \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f *\/\n    #generate-button {\n        width: 100%;\n        padding: 12px;\n        background-color: #0B638B;\n        color: white;\n        border: none;\n        border-radius: 5px;\n        font-size: 16px;\n        cursor: pointer;\n        margin-top: 10px;\n        transition: background-color 0.3s ease;\n    }\n    \n    #generate-button:hover {\n        background-color: #065a71;\n    }\n    \n    \/* \u041a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u0434\u043b\u044f \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0456\u0432 *\/\n    .solution-container {\n        background-color: #ffffff;\n        padding: 20px;\n        margin-top: 15px;\n        margin-bottom: 15px;\n        font-size: 16px;\n        color: #333;\n        line-height: 1.6;\n        max-width: 800px;\n        margin-left: auto;\n        margin-right: auto;\n        overflow-x: auto;\n    }\n    \n    \/* \u0410\u043d\u0456\u043c\u0430\u0446\u0456\u044f \u0437\u0430\u0432\u0430\u043d\u0442\u0430\u0436\u0435\u043d\u043d\u044f *\/\n    .loader {\n        display: block;\n        margin: 20px auto;\n        border: 8px solid #f3f3f3;\n        border-top: 8px solid #0B638B;\n        border-radius: 50%;\n        width: 75px;\n        height: 75px;\n        animation: spin 1s linear infinite;\n    }\n    \n    @keyframes spin {\n        0% { transform: rotate(0deg); }\n        100% { transform: rotate(360deg); }\n    }\n    \n    \/* \u041f\u043e\u0432\u0456\u0434\u043e\u043c\u043b\u0435\u043d\u043d\u044f \u043f\u0440\u043e \u043f\u043e\u043c\u0438\u043b\u043a\u0443 *\/\n    .error-message {\n        background-color: #fdecea;\n        color: #b71c1c;\n        border-left: 4px solid #b71c1c;\n        border-radius: 5px;\n        padding: 15px;\n        margin-top: 10px;\n        font-size: 16px;\n        display: none;\n    }\n    \n    .error-message.show {\n        display: block;\n        animation: fadeIn 0.5s ease-in-out;\n    }\n    \n    \/* \u0410\u0434\u0430\u043f\u0442\u0430\u0446\u0456\u044f \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n    @media (max-width: 768px) {\n        .calculator-container {\n            padding: 15px;\n        }\n    \n        .padBtn {\n            font-size: 12px;\n        }\n    \n        #generate-button {\n            font-size: 12px;\n        }\n        \n        .formula {\n            font-size: 14px;\n            padding: 4px;\n        }\n    }\n    \n    @media (max-width: 480px) {\n        .calcKeypad {\n            flex-wrap: wrap;\n        }\n    \n        .padBtn {\n            max-width: 48%;\n            margin-bottom: 5px;\n            font-size: 10px;\n        }\n    \n        input, select {\n            font-size: 14px;\n        }\n    \n        #generate-button {\n            font-size: 10px;\n        }\n        \n        .formula {\n            font-size: 12px;\n            padding: 3px;\n        }\n    }\n    \/* \u0421\u0442\u0438\u043b\u044c \u0434\u043b\u044f SVG-\u0433\u0440\u0430\u0444\u0456\u043a\u0430 *\/\n    #graph-svg {\n        width: 100%;\n        max-width: 700px;\n        height: auto;\n        display: block;\n        margin: 50px 0px auto;\n        background-color: #ffffff;\n    }\n    \n    .formula {\n        font-family: 'STIX Two Math', serif; \/* \u0428\u0440\u0438\u0444\u0442 \u0434\u043b\u044f \u0444\u043e\u0440\u043c\u0443\u043b *\/\n        background-color: #ffffff; \/* \u0411\u0456\u043b\u0438\u0439 \u0444\u043e\u043d *\/\n        padding: 5px; \/* \u0412\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n        margin-bottom: 5px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u043c\u0456\u0436 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438 *\/\n        overflow-x: auto; \/* \u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430 \u043f\u0440\u043e\u043a\u0440\u0443\u0442\u043a\u0430 \u0434\u043b\u044f \u0432\u0435\u043b\u0438\u043a\u0438\u0445 \u0444\u043e\u0440\u043c\u0443\u043b *\/\n        font-size: 16px;\n    }\n    \n    \/* \u0421\u0442\u0438\u043b\u0456 \u0434\u043b\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0456 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0456\u0432 *\/\n    .result-table {\n        width: 100%;\n        border-collapse: collapse;\n        margin-top: 20px;\n        font-family: Arial, sans-serif;\n    }\n    \n    .result-table thead {\n        background-color: #0B638B;\n        color: white;\n    }\n    \n    .result-table th, .result-table td {\n        border: 1px solid #ddd;\n        padding: 3px;\n        text-align: center;\n        font-size: 14px;\n    }\n    \n    .result-table tbody tr:nth-child(even) {\n        background-color: #f2f8fc;\n    }\n    \n    .result-table tbody tr:nth-child(odd) {\n        background-color: white;\n    }\n    \n    .result-table tbody tr:hover {\n        background-color: #cce7f5;\n        transition: 0.3s ease-in-out;\n    }\n    \n    \/* \u0410\u0434\u0430\u043f\u0442\u0438\u0432\u043d\u0456 \u0441\u0442\u0438\u043b\u0456 \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n    @media (max-width: 768px) {\n        .result-table {\n            font-size: 12px;\n        }\n    \n        .result-table th, .result-table td {\n            padding: 5px;\n            font-size: 12px;\n        }\n        .formula {\n            font-size: 12px;\n            padding: 3px; \/* \u0412\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n            margin-bottom: 3px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u043c\u0456\u0436 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438 *\/\n        }\n        .solution-container h2 {\n            font-size: 24px; \/* \u041c\u0435\u043d\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        }\n        .solution-container h3 {\n            font-size: 20px; \/* \u041c\u0435\u043d\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        }\n        .solution-container {\n            font-size: 14px; \/* \u0417\u043c\u0435\u043d\u0448\u0435\u043d\u043d\u044f \u0440\u043e\u0437\u043c\u0456\u0440\u0443 \u0442\u0435\u043a\u0441\u0442\u0443 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        }\n    }\n    \n    @media (max-width: 480px) {\n        .result-table {\n            font-size: 8px;\n        }\n    \n        .result-table th, .result-table td {\n            padding: 1px;\n            font-size: 8px;\n        }\n        .formula {\n            font-size: 8px;\n            padding: 1px; \/* \u0412\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n            margin-bottom: 1px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u043c\u0456\u0436 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438 *\/\n        }\n        .solution-container h2 {\n            font-size: 20px; \/* \u041c\u0435\u043d\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        }\n        .solution-container h3 {\n            font-size: 16px; \/* \u041c\u0435\u043d\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        }\n        .solution-container {\n            font-size: 13px; \/* \u0417\u043c\u0435\u043d\u0448\u0435\u043d\u043d\u044f \u0440\u043e\u0437\u043c\u0456\u0440\u0443 \u0442\u0435\u043a\u0441\u0442\u0443 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        }\n    }\n<\/style>\n\n<script>\n    const MQ = MathQuill.getInterface(2);\n    const inputSpan = document.getElementById('inputField');\n    let answerMathField = MQ.MathField(inputSpan, {\n      spaceBehavesLikeTab: true,\n      handlers: {\n        edit: function() {\n          answerMathField.focus();\n        }\n      }\n    });\n\n    function addSymbol(symbol) {\n      answerMathField.write(symbol);\n      answerMathField.focus();\n    }\n\n    \/\/ \u041f\u0440\u0438 \u0432\u0456\u0434\u043f\u0440\u0430\u0432\u0446\u0456 \u0444\u043e\u0440\u043c\u0438, \u0437\u0430\u043f\u0438\u0441\u0443\u0454\u043c\u043e \u0432\u043c\u0456\u0441\u0442 MathField \u0443 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u0435 \u043f\u043e\u043b\u0435 \u0444\u043e\u0440\u043c\u0438\n    document.querySelector('.calculateBtn').addEventListener('click', function() {\n      document.getElementById('latexExpression').value = answerMathField.latex();\n    });\n\n\n\n\n    function calculateIntegral() {\n        var func = answerMathField.latex();\n        var lowLimit = document.getElementById('lower_limit');\n        var uppLimit = document.getElementById('upper_limit');\n        var numPartitions = document.getElementById('num_partitions');\n\n        \/\/ \u0406\u043d\u0456\u0446\u0456\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u0434\u0432\u043e\u0432\u0438\u043c\u0456\u0440\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0438\u0432\u0443 \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0432\u0432\u0435\u0434\u0435\u043d\u0438\u0445 \u043a\u043e\u0440\u0438\u0441\u0442\u0443\u0432\u0430\u0447\u0435\u043c \u0434\u0430\u043d\u0438\u0445\n        var enteredData = [];\n        \/\/ \u0414\u043e\u0434\u0430\u0432\u0430\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0434\u043e \u0434\u0432\u043e\u0432\u0438\u043c\u0456\u0440\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0438\u0432\u0443\n        enteredData.push(func || '');\n        enteredData.push(parseFloat(lowLimit.value) || 0);\n        enteredData.push(parseFloat(uppLimit.value) || 0);\n        enteredData.push(parseFloat(numPartitions.value) || 0);\n        \n        sendDataToServer(enteredData);\n        \n        transferX = document.getElementById(\"X\");\n        transferY = document.getElementById(\"Y\");\n        size = document.getElementById(\"SIZE\");\n        transferX.value = 0;\n        transferY.value = 0;\n        size.value = 0;\n    }\n    \n\nfunction drawGraphAndTrapezoids(graphData, trapezoidsData) {\n    const svgWidth = 700;\n    const svgHeight = 400;\n    const margin = { top: 20, right: 20, bottom: 30, left: 50 };\n\n    const width = svgWidth - margin.left - margin.right;\n    const height = svgHeight - margin.top - margin.bottom;\n\n    let formattedGraphData = convertDataForSVG(graphData);\n    let formattedTrapezoidsData = convertTrapezoidsForSVG(trapezoidsData);\n\n    const xMin = d3.min(formattedGraphData, d => d.x);\n    const xMax = d3.max(formattedGraphData, d => d.x);\n    let yMin = d3.min(formattedGraphData, d => d.y);\n    yMin = yMin > 0 ? 0 : yMin;\n    let yMax = d3.max(formattedGraphData, d => d.y);\n    yMax = yMax < 0 ? 0 : yMax;\n\n    \/\/ Clear and set up the SVG element\n    const svg = d3.select(\"#graph-svg\")\n        .html(\"\") \/\/ Clear previous contents\n        .attr(\"width\", svgWidth)\n        .attr(\"height\", svgHeight)\n        .append(\"g\")\n        .attr(\"transform\", `translate(${margin.left},${margin.top})`);\n\n    const xScale = d3.scaleLinear()\n        .domain([xMin, xMax])\n        .range([0, width]);\n\n    const yScale = d3.scaleLinear()\n        .domain([yMin, yMax])\n        .range([height, 0]);\n\n    \/\/ Append the axes\n    svg.append(\"g\")\n        .attr(\"transform\", `translate(0,${height})`)\n        .call(d3.axisBottom(xScale))\n        .selectAll(\"path, line\")\n        .attr(\"stroke\", \"#E8E8E8\");\n\n    svg.append(\"g\")\n        .call(d3.axisLeft(yScale))\n        .selectAll(\"path, line\")\n        .attr(\"stroke\", \"#E8E8E8\");\n\n    \/\/ Add grid lines\n    svg.append(\"g\")\n        .attr(\"class\", \"grid\")\n        .call(\n            d3.axisLeft(yScale)\n                .tickSize(-width)\n                .tickFormat(\"\")\n                .ticks(10)\n        )\n        .selectAll(\"line\")\n        .attr(\"stroke\", \"#E8E8E8\")\n        .attr(\"stroke-opacity\", 1)\n        .filter((d, i, nodes) => d !== yMax)\n        .attr(\"stroke-dasharray\", \"\");\n\n    svg.selectAll(\".domain\")\n        .attr(\"stroke\", \"#E8E8E8\");\n\n    \/\/ Define the area between the graph and the OX axis\n    const area = d3.area()\n        .x(d => xScale(d.x))\n        .y0(yScale(0)) \/\/ Set the OX axis at y=0\n        .y1(d => yScale(d.y));\n\n    \/\/ Append the filled area (95% transparent)\n    svg.append(\"path\")\n        .datum(formattedGraphData)\n        .attr(\"fill\", \"#0b638b\")\n        .attr(\"fill-opacity\", 0.05)\n        .attr(\"d\", area);\n\n    \/\/ Define the line generator for the graph\n    const line = d3.line()\n        .x(d => xScale(d.x))\n        .y(d => yScale(d.y));\n\n    \/\/ Append the line graph\n    svg.append(\"path\")\n        .datum(formattedGraphData)\n        .attr(\"fill\", \"none\")\n        .attr(\"stroke\", \"#0b638b\")\n        .attr(\"stroke-width\", 3)\n        .attr(\"d\", line);\n\n    \/\/ Draw trapezoids as polygons\n    svg.selectAll(\".trapezoid\")\n        .data(formattedTrapezoidsData)\n        .enter()\n        .append(\"polygon\")\n        .attr(\"points\", d => {\n            \/\/ Define the four points of the trapezoid:\n            \/\/ (x, y), (next_x, next_y), (next_x, 0), (x, 0)\n            return `${xScale(d.x)},${yScale(d.y)} \n                    ${xScale(d.next_x)},${yScale(d.next_y)} \n                    ${xScale(d.next_x)},${yScale(0)} \n                    ${xScale(d.x)},${yScale(0)}`;\n        })\n        .attr(\"fill\", \"rgba(255, 0, 0, 0.05)\")  \/\/ Red fill with 95% transparency\n        .attr(\"stroke\", \"#FF0000\") \/\/ Red border\n        .attr(\"stroke-width\", 0.5);  \/\/ Border thickness\n\n    \/\/ Add the vertical dotted line and point display functionality\n    const focusLine = svg.append(\"line\")\n        .attr(\"stroke\", \"gray\")\n        .attr(\"stroke-dasharray\", \"3,3\")\n        .attr(\"y1\", 0)\n        .attr(\"y2\", height)\n        .style(\"display\", \"none\");\n\n    const focusCircle = svg.append(\"circle\")\n        .attr(\"r\", 4)\n        .attr(\"fill\", \"#0b638b\")\n        .style(\"display\", \"none\");\n\n    const focusText = svg.append(\"text\")\n        .attr(\"fill\", \"#333\")\n        .style(\"display\", \"none\");\n\n    svg.append(\"rect\")\n        .attr(\"width\", width)\n        .attr(\"height\", height)\n        .attr(\"fill\", \"none\")\n        .attr(\"pointer-events\", \"all\")\n        .on(\"mousemove\", mousemove)\n        .on(\"mouseout\", () => {\n            focusLine.style(\"display\", \"none\");\n            focusCircle.style(\"display\", \"none\");\n            focusText.style(\"display\", \"none\");\n        });\n\n    function mousemove(event) {\n        const [mouseX] = d3.pointer(event);\n        const xValue = xScale.invert(mouseX);\n\n        if (xValue < xMin || xValue > xMax) {\n            focusLine.style(\"display\", \"none\");\n            focusCircle.style(\"display\", \"none\");\n            focusText.style(\"display\", \"none\");\n            return;\n        }\n\n        const closestPoint = formattedGraphData.reduce((prev, curr) =>\n            Math.abs(curr.x - xValue) < Math.abs(prev.x - xValue) ? curr : prev\n        );\n\n        const xPos = xScale(closestPoint.x);\n        const yPos = yScale(closestPoint.y);\n\n        if (yPos < 0 || yPos > height) {\n            focusLine.style(\"display\", \"none\");\n            focusCircle.style(\"display\", \"none\");\n            focusText.style(\"display\", \"none\");\n            return;\n        }\n\n        focusLine\n            .attr(\"x1\", xPos)\n            .attr(\"x2\", xPos)\n            .attr(\"stroke-dasharray\", \"1,3\")\n            .style(\"display\", null);\n\n        focusCircle\n            .attr(\"cx\", xPos)\n            .attr(\"cy\", yPos)\n            .style(\"display\", null);\n\n        const textPadding = 10;\n        let textX = xPos + textPadding;\n        let textY = yPos - textPadding;\n\n        if (xPos + 100 > width) {\n            textX = xPos - 100;\n        }\n\n        if (yPos - 20 < 0) {\n            textY = yPos + textPadding;\n        }\n\n        focusText\n            .attr(\"x\", textX)\n            .attr(\"y\", textY)\n            .text(`x: ${closestPoint.x.toFixed(2)}, y: ${closestPoint.y.toFixed(2)}`)\n            .attr(\"font-size\", 10)\n            .style(\"display\", null);\n    }\n}\n\n\/\/ Helper function to convert server data to {x, y} format\nfunction convertDataForSVG(graphData) {\n    return graphData.map(point => ({ x: point[0], y: point[1] }));\n}\n\n\/\/ Helper function to convert trapezoids for SVG (separate from rectangles)\nfunction convertTrapezoidsForSVG(trapezoidsData) {\n    return trapezoidsData.map(trap => {\n        return {\n            x: trap[0],      \/\/ x is the starting x-coordinate\n            y: trap[2],      \/\/ y is the height at the starting point\n            next_x: trap[1], \/\/ next_x is the next x-coordinate (end of trapezoid)\n            next_y: trap[3]  \/\/ next_y is the height at the end point\n        };\n    });\n}\n\n\/\/-------------------------------------------------------------\n    \n    function renderMathJax() {\n        MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n    }\n    \n    function sendDataToServer(enteredData) {\n        var loading = document.getElementById('loading');\n        var resultC = document.getElementById('fcontainer');\n        var resultCalc = document.getElementById('calculation-results');\n        var errorBlock = document.getElementById('error-block'); \/\/ \u0411\u043b\u043e\u043a \u0434\u043b\u044f \u043f\u043e\u0432\u0456\u0434\u043e\u043c\u043b\u0435\u043d\u044c \u043f\u0440\u043e \u043f\u043e\u043c\u0438\u043b\u043a\u0438\n        \n        resultC.innerHTML = '';\n        errorBlock.classList.remove('show'); \/\/ \u041f\u0440\u0438\u0445\u043e\u0432\u0443\u0454\u043c\u043e \u0431\u043b\u043e\u043a \u043f\u043e\u043c\u0438\u043b\u043e\u043a \u043f\u0435\u0440\u0435\u0434 \u043f\u043e\u0447\u0430\u0442\u043a\u043e\u043c \u043d\u043e\u0432\u043e\u0433\u043e \u0437\u0430\u043f\u0438\u0442\u0443\n        errorBlock.innerHTML = ''; \n        \n        \/\/var generateButton = document.getElementById(\"generate-button\");\n        \n        \/\/if (generateButton.disabled) {\n        \/\/    return; \/\/ \u0417\u0430\u043f\u043e\u0431\u0456\u0433\u0430\u0439\u0442\u0435 \u0431\u0430\u0433\u0430\u0442\u043e\u0440\u0430\u0437\u043e\u0432\u0438\u043c \u043d\u0430\u0442\u0438\u0441\u043a\u0430\u043d\u043d\u044f\u043c \u043f\u0456\u0434 \u0447\u0430\u0441 \u0441\u0442\u0432\u043e\u0440\u0435\u043d\u043d\u044f \u0432\u043c\u0456\u0441\u0442\u0443\n        \/\/}\n        \n        \/\/generateButton.disabled = true;\n    \n        loading.style.display = 'block';\n        resultCalc.style.display = 'none';\n    \n        var formData = new FormData();\n        formData.append('action', 'integration_by_trapezium_method');\n        formData.append('enteredData', JSON.stringify(enteredData));\n\n        fetch('\/en\/wp-admin\/admin-ajax.php', {\n            method: 'POST',\n            body: formData\n        })\n        .then(response => {\n           if (!response.ok) {\n                throw new Error('Network response was not ok');\n            }\n            return response.json();\n        })\n        .then(data => {\n            loading.style.display = 'none';\n            if (data.success) {\n                if (Array.isArray(data.integral)) {\n                    const messages = [\n    \"Your Result is Ready! Here\u2019s the Value of Your Definite Integral\",\n    \"Here\u2019s the Answer! The Result of the Definite Integral Calculation with Our Calculator\",\n    \"Get Your Integral Result Right Now \u2013 Fast, Accurate, and Effortless!\",\n    \"Congratulations! Your Definite Integral Calculation is Complete \u2013 Here\u2019s the Answer!\",\n    \"The Calculation Result is Already on the Screen! Thank You for Using Our Online Calculator\"\n  ];\n                    const randomIndex = Math.floor(Math.random() * messages.length);\n                    resultC.innerHTML += '<h2><center>' + messages[randomIndex] + '<\/center><\/h2><svg id=\"graph-svg\" width=\"800\" height=\"400\"><\/svg>';\n                    \n                    for (let i = 0; i < data.integral[1].length; i++) {\n                        if (data.integral[2][i]) {\n                            resultC.innerHTML += data.integral[2][i];\n                        }\n                        resultC.innerHTML += '<div class=\"formula\">' + data.integral[1][i] + '<\/div>';\n                    }\n                    \n                    var lowLimit = document.getElementById('lower_limit');\n                    var uppLimit = document.getElementById('upper_limit');\n                    \n                    drawGraphAndTrapezoids(data.integral[3][\"graph\"], data.integral[3][\"trapezoids\"]);\n                } else {\n                    resultC.innerHTML += '<div class=\"formula\">' + data.integral + '<\/div>';\n                }\n                renderMathJax();\n                resultCalc.style.display = 'block';\n            } else {\n                showError(data.error);\n            }\n        })\n        .catch(error => {\n            loading.style.display = 'none';\n            showError(error.message); \/\/ \u0412\u0438\u043a\u043b\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0456\u0457 \u0434\u043b\u044f \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f \u043f\u043e\u043c\u0438\u043b\u043a\u0438\n        });\n    }\n    \/\/ \u0424\u0443\u043d\u043a\u0446\u0456\u044f \u0434\u043b\u044f \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f \u043f\u043e\u0432\u0456\u0434\u043e\u043c\u043b\u0435\u043d\u043d\u044f \u043f\u0440\u043e \u043f\u043e\u043c\u0438\u043b\u043a\u0443\n    function showError(message) {\n        var errorBlock = document.getElementById('error-block');\n        errorBlock.textContent = message;\n        errorBlock.classList.add('show'); \/\/ \u0412\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0430\u0454\u043c\u043e \u0431\u043b\u043e\u043a \u0437 \u043f\u043e\u0432\u0456\u0434\u043e\u043c\u043b\u0435\u043d\u043d\u044f\u043c \u043f\u0440\u043e \u043f\u043e\u043c\u0438\u043b\u043a\u0443\n    }\n<\/script>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e3a6717 elementor-widget elementor-widget-html\" data-id=\"e3a6717\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"h2-title2\">How Does the Trapezium Rule Calculator Work? Let\u2019s Break It Down Together!<\/h2>\n<img decoding=\"async\" class=\"aligncenter wp-image-10020256 size-full\" src=\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2024\/09\/trapezium-rule-calculator.jpg\" alt=\"trapezium rule calculator, trapezium rule formula calculator, trapezium rule integration calculator\" width=\"150\" height=\"150\" \/>\n<p class=\"calculator-p\">The <strong>trapezium rule calculator<\/strong> is a simple yet effective tool for <strong>approximating the value of definite <a title=\"Integral\" href=\"https:\/\/en.wikipedia.org\/wiki\/Integral\" target=\"_blank\" rel=\"nofollow noopener\">integrals<\/a><\/strong>. It uses a <strong>geometric approach<\/strong> by dividing the area under the curve into a series of trapezoids, each helping to estimate the area. With this calculator, you can easily input the integration limits and the function you want to integrate. The result is computed quickly and accurately using a <strong>mathematical algorithm<\/strong> based on the <a title=\"Trapezium Rule Formula\" href=\"https:\/\/www.mathros.net.ua\/en\/trapezium-rule.html\">trapezium rule<\/a>.<\/p>\n<p class=\"calculator-p\">So, how does this all work in practice? First, you enter the <strong>required data<\/strong>, and the calculator automatically divides the integration range into <strong>equal segments<\/strong>. For each segment, a trapezoid is drawn, and its area is added to the total sum. This way, the calculator approximates the integral by estimating the <strong>area under the curve<\/strong>. The approximation becomes more accurate as the <strong>number of trapezoids<\/strong> increases.<\/p>\n<p class=\"calculator-p\">Once the calculations are complete, the calculator displays the <strong>result on the screen<\/strong> along with a <strong>graph of the integrated function<\/strong>. This visualization helps to better understand how the trapezium method works on each individual interval. So, you get not only a <strong>numerical result<\/strong> but also a <strong>clear visual representation<\/strong> of the integration process, making this tool both <strong>convenient<\/strong> and <strong>easy to use<\/strong> for everyone.<\/p>\n<style>\n    .h2-title2 {\n        text-align: center; \/* \u0426\u0435\u043d\u0442\u0440\u0443\u0432\u0430\u043d\u043d\u044f \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0430 *\/\n        color: gray; \/* \u0417\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0441\u0456\u0440\u043e\u0433\u043e \u043a\u043e\u043b\u044c\u043e\u0440\u0443 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-size: 28px; \/* \u0417\u0430\u043b\u0438\u0448\u0430\u0454\u043c\u043e \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-weight: 700; \/* \u0420\u043e\u0431\u0438\u043c\u043e \u0442\u0435\u043a\u0441\u0442 \u0436\u0438\u0440\u043d\u0438\u043c \u0434\u043b\u044f \u0430\u043a\u0446\u0435\u043d\u0442\u0443 *\/\n        line-height: 1.4; 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Use Our Online Calculator for Instant and Easy Results! Integrand Function (e.g.,<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-centered.php","meta":{"footnotes":""},"class_list":["post-1120","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages\/1120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/comments?post=1120"}],"version-history":[{"count":71,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages\/1120\/revisions"}],"predecessor-version":[{"id":1892,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages\/1120\/revisions\/1892"}],"wp:attachment":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/media?parent=1120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}