{"id":57192,"date":"2025-03-13T20:31:53","date_gmt":"2025-03-13T15:01:53","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=57192"},"modified":"2026-03-02T21:24:45","modified_gmt":"2026-03-02T15:54:45","slug":"evaluate-indefinite-and-definite-integrals-and-volume-of-the-solid-using-geogebra-classic-5","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=57192","title":{"rendered":"Evaluate indefinite and definite integrals and volume of the solid using Geogebra classic 5"},"content":{"rendered":"\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-89bfda0d449bddcb20c4924e685a3000\">Aim:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ \\text{Graph the functions}\\  \\hspace{22cm}\\\\ \\hspace{1cm} \\text{c (constant),  x^n,  n \u2208 R, sin x, cos x},\\ sec^2\\ x,\\ cosec^2\\ x,\\ \\hspace{15cm}\\\\ \\text{secx tanx and cosecxcotx.   Find their indefinite integrals}\\ \\hspace{10cm}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\text{Evaluate the definite integral}\\ \\int_{a}^{b} x^2\\ dx\\ \\hspace{15cm}\\\\ \\text{and relate it to the area under the curve y=f(x)}\\ \\hspace{13cm}\\\\ \\text{between x &#8211; axis, x = a and x = b}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ \\text{Find the volume of the solid generated by the revolution}\\  \\hspace{15cm}\\\\ \\text{of the area bounded by y=f(x)}\\ \\hspace{10cm}\\\\ \\text{x &#8211; axis, x = a and x = b about x axis}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-caaadd60b535c837691a2eb0c3ab170e\">Procedure:<\/h5>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>1. Indefinite Integrals.<\/strong><\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 (by double clicking on the icon)}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To draw the graph of the function}\\  x^2\\  by\\ using\\ input\\ bar\\ \\hspace{10cm}\\\\ \\text{to type x^2 and press the Enter key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{To evaluate the indefinite integral of the given function f(x)}\\hspace{13cm}\\\\ \\text{by  using input command type integral f(x) and press the  Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{create an input box for the function f(x)}\\ \\hspace{15cm}\\\\ \\text{and link with the given function f(x)}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{use input box enters the given functions}\\ \\hspace{15cm}\\\\ \\text{and observe the graph of indefinite integrals}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center\">output for indefinite integrals<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Function f(x)<\/td><td><mathml>\\[\\int f(x)\\ dx\\]<\/mathml><\/td><\/tr><tr><td>5<\/td><td>5x<\/td><\/tr><tr><td>x<sup>2<\/sup><\/td><td>1\/3 x<sup>3<\/sup><\/td><\/tr><tr><td>e<sup>x<\/sup><\/td><td>e<sup>x<\/sup><\/td><\/tr><tr><td>sin x<\/td><td>&#8211; cos x<\/td><\/tr><tr><td>cos x <\/td><td>sin x<\/td><\/tr><tr><td>sec<sup>2<\/sup>x<\/td><td>tan x<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<h5 class=\"wp-block-heading\">2. <strong>Definite Integrals.<\/strong><\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 window}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To draw the graph of the function}\\  x^2\\  by\\ using\\ input\\ bar\\ \\hspace{10cm}\\\\ \\text{to type x^2 and press the Enter key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{Create two number sliders a and b.}\\ \\hspace{15cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{Create two input boxes link with slider a and b.}\\ \\hspace{15cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{Create an input box for the given function link with f(x)}\\ \\ \\hspace{15cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{Evaluate the definite integral}\\ \\int_{0}^{3}\\ x^3\\ dx\\ \\hspace{15cm}\\\\ \\text{and relate it to the area under the curve y =}\\ x^2\\ \\text{between x &#8211; axis,}\\ \\hspace{10cm}\\\\ \\text{x=0 and x=3. By using the input command A=Integral(f,0,3).}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{Drag or move the sliders a and b,}\\ \\hspace{15cm}\\\\ \\text{observe the area under curve}\\ \\hspace{12cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{Change the values of f(x), a and b in the}\\ \\hspace{15cm}\\\\ \\text{respective input boxes and record the}\\ \\hspace{10cm}\\\\ \\text{corresponding values of areas.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center\">output for definite integrals and area under the curve<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Function f(x)<\/td><td>x = a<\/td><td>x = b<\/td><td><mathml>\\[\\int_{a}^{b} f(x)\\ dx\\]<\/mathml><\/td><td>Area between the f(x), y = 0, x = a and x = b<\/td><\/tr><tr><td>x<sup>2<\/sup><\/td><td>0<\/td><td>3<\/td><td><mathml>\\[ \\int_{0}^{3} x^2\\ dx\\]<\/mathml><\/td><td>9<\/td><\/tr><tr><td>x<\/td><td>0<\/td><td>6<\/td><td><mathml>\\[\\int_{0}^{6} x\\ dx\\]<\/mathml><\/td><td>18<\/td><\/tr><tr><td>x<sup>3<\/sup><\/td><td>1<\/td><td>2<\/td><td><mathml>\\[\\int_{0}^{6} x^3\\ dx\\]<\/mathml><\/td><td>3.75<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">3. <strong>Volume of the Solid.<\/strong><\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 window and 3D graphics window}\\ \\hspace{14cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To draw the graph of the given function x}\\ \\hspace{15cm}\\\\ \\text{in the interval x = 0 to x = 3 by using the}\\ \\hspace{10cm}\\\\ \\text{input bar to type if(0&lt;=x&lt;=3, x)}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{Create an angle slider for \u03b1.}\\ \\hspace{15cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To generate the surface of the solid formed by the}\\ \\hspace{15cm}\\\\ \\text{revolution of the area bounded by y =x, x-axis, x = 0 and x = 3}\\ \\hspace{10cm}\\\\ \\text{about x &#8211; axis by using the command Surface{f,\u03b1, xAxis}}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{Right click on the slider, choose Animation on.}\\ \\ \\hspace{15cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To find the volume of the solid by}\\ \\hspace{15cm}\\\\ \\text{using the input command V = pi Integral(f^2,0,3)}\\ \\hspace{10cm}\\\\ \\text{or V= \u03c0 Integral(f^2,0,3)}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{Rotate the line y = x and the surface}\\ \\hspace{15cm}\\\\ \\text{revolution of the area bounded by y =x, x-axis, x = 0 and x = 3}\\ \\hspace{10cm}\\\\ \\text{about x &#8211; axis by using the command Surface{f,\u03b1, xAxis}}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center\">output for the volume of a solid revolution of surface generated by a curve<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Function f(x)<\/td><td>x = a<\/td><td>x = b<\/td><td><mathml>\\[Volume\\ =\\ \\pi\\  \\int_{a}^{b} (f(x))^2\\ dx\\]<\/mathml><\/td><\/tr><tr><td>x<\/td><td>0<\/td><td>3<\/td><td>28.27<\/td><\/tr><tr><td>x<sup>2<\/sup><\/td><td>0<\/td><td>3<\/td><td>152.68<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<p><iframe width=\"878\" height=\"549\" src=\"https:\/\/www.youtube.com\/embed\/no5UhNf853g?list=PLQIom4Rz29vyp5ZiCGuc0-zCEqs8Pvslf\" title=\"Evaluating Indefinite, Definite Integrals and volume of solid by using Geogebra Classic - 5 - Telugu\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"\"><\/iframe><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Procedure: 1. Indefinite Integrals. Output: output for indefinite integrals Function f(x) \\[\\int f(x)\\ dx\\] 5 5x x2 1\/3 x3 ex ex sin x &#8211; cos x cos x sin x sec2x tan x 2. Definite Integrals. Output: output for definite integrals and area under the curve Function f(x) x = a x = b [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":57284,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[711788743],"tags":[],"class_list":["post-57192","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-applied-mathematics-i"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Evaluate indefinite and definite integrals and volume of the solid using Geogebra classic 5 - YANAMTAKSHASHILA<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/yanamtakshashila.com\/?p=57192\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Evaluate indefinite and definite integrals and volume of the solid using Geogebra classic 5 - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"Aim: Procedure: 1. Indefinite Integrals. Output: output for indefinite integrals Function f(x) [int f(x) dx] 5 5x x2 1\/3 x3 ex ex sin x &#8211; cos x cos x sin x sec2x tan x 2. Definite Integrals. 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Indefinite Integrals. Output: output for indefinite integrals Function f(x) [int f(x) dx] 5 5x x2 1\/3 x3 ex ex sin x &#8211; cos x cos x sin x sec2x tan x 2. Definite Integrals. Output: output for definite integrals and area under the curve Function f(x) x = a x = b [&hellip;]","og_url":"https:\/\/yanamtakshashila.com\/?p=57192","og_site_name":"YANAMTAKSHASHILA","article_publisher":"https:\/\/www.facebook.com\/profile.php?id=100063680185552","article_author":"https:\/\/www.facebook.com\/profile.php?id=100063680185552","article_published_time":"2025-03-13T15:01:53+00:00","article_modified_time":"2026-03-02T15:54:45+00:00","og_image":[{"width":1200,"height":675,"url":"https:\/\/yanamtakshashila.com\/wp-content\/uploads\/2025\/03\/Screenshot-2025-03-17-162055.png","type":"image\/png"}],"author":"rajuviswa","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rajuviswa","Est. reading time":"4 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