{"id":29938,"date":"2022-05-19T21:31:03","date_gmt":"2022-05-19T16:01:03","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=29938"},"modified":"2022-06-13T19:45:38","modified_gmt":"2022-06-13T14:15:38","slug":"solutions-to-internal-assessment-ii-for-engineering-mathematics-ii","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=29938","title":{"rendered":"SOLUTIONS TO INTERNAL ASSESSMENT &#8211; II FOR ENGINEERING MATHEMATICS-II"},"content":{"rendered":"\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ A}\\]<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\">\\[Marks:\\ 6\\ \u00d7\\ 1\\ =\\ 6\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ \\color{Red}{Evaluate: \\int(x^2 -x + 5)\\ dx}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/09\/4-1-integration-decomposition-method\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/09\/4-1-integration-decomposition-method\">Refer Example 1 under Integration Decomposition Method<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\color{red}{Evaluate\\ :\\ \\int\\ \\frac{2x}{1 + x^2}}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/12\/4-2-integration-by-substitution\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/12\/4-2-integration-by-substitution\/\">Refer Example 3 under Integration By Substitution<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ \\color{red}{Evaluate\\ :\\ \\int\\ \\frac{dx}{x^2 + 4}}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/16\/4-3-standard-integrals\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/16\/4-3-standard-integrals\/\">Refer Example No. 1 (STANDARD INTEGRALS)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ \\color{Red}{Evaluate:\\ \\int x\\ sin\\ x\\ dx}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/5-1-integration-by-parts\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/5-1-integration-by-parts\/\">Refer Example No. 1 INTEGRATION BY PARTS<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ \\color{red}{Evaluate:\\ \\int x^3\\ sin\\ x\\ dx}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/bernoulllis-formula\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/bernoulllis-formula\/\">Refer Example No. 1 (BERNOULLI&#8217;S FORMULA)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ \\color{red}{Evaluate\\ :\\ \\int_1^2 x^2\\ dx}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/21\/definite-integrals\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/21\/definite-integrals\/\">Refer Example No. 1 DEFINITE INTEGRALS<\/a><\/p>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-format=\"autorelaxed\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"6771622407\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ B}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Marks:\\ 7\\ \u00d7\\ 2\\ =\\ 14\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[7.\\ \\color{red}{Evaluate: \\int(x^2 + x + 1) ( x^2 &#8211; x + 1)\\ dx}\\ \\hspace{55cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/09\/4-1-integration-decomposition-method\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/09\/4-1-integration-decomposition-method\">Refer Example 6 under Integration Decomposition Method<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[8.\\ \\color {red}{Evaluate: \\int \\frac{sin^2 x}{ 1+ cos x} \\ dx}\\  \\hspace{15cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2022\/04\/15\/integration-decomposition-method-exercise-problems-with-solutions\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2022\/04\/15\/integration-decomposition-method-exercise-problems-with-solutions\/\">Refer Example 6 under Integration Decomposition Method (Excercise Problems with Solutions)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[9.\\ \\color{red}{Evaluate\\ :\\ \\int\\ (x^2 + x + 1)^5\\ (2x + 1) dx}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<p class=\"wp-block-coblocks-highlight\"><mark class=\"wp-block-coblocks-highlight__content\">Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/12\/4-2-integration-by-substitution\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/12\/4-2-integration-by-substitution\/\">Refer Example 3 under Integration By Substitution<\/a><\/mark><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[10.\\  \\color{red}{Evaluate:\\ \\int \\frac{dx}{4x^2 + 9}}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/16\/4-3-standard-integrals\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/16\/4-3-standard-integrals\/\">Refer Example No. 2 (STANDARD INTEGRALS)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[11.\\ \\color{red}{Evaluate:\\ \\int e^{nx}\\ dx}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/5-1-integration-by-parts\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/5-1-integration-by-parts\/\">Refer Example No. 3 INTEGRATION BY PARTS<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[12.\\ \\color{red}{\\int x^3\\ cos\\ x\\ dx}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/bernoulllis-formula\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/bernoulllis-formula\/\">Refer Example No. 2 (BERNOULLI&#8217;S FORMULA)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[13.\\ \\color{red}{Evaluate\\ :\\ \\int_0^\\frac{\\pi}{2} sin^3 x\\ dx}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/21\/definite-integrals\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/21\/definite-integrals\/\">Refer Example No. 6 DEFINITE INTEGRALS<\/a><\/p>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<!-- Ad1 -->\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"8240817448\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ C}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[14.\\ \\color{red}{i)\\ Evaluate:\\ \\hspace{2cm}\\ (i)\\ \\int \\frac{cos^2 x}{ 1- sin x} \\ dx\\ \\hspace{2cm}\\ (ii)\\ \\int sin 5x\\  cos 2x\\ dx}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/09\/4-1-integration-decomposition-method\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/09\/4-1-integration-decomposition-method\/\">Refer Example No. 5 and Example No. 8  under Trigonometry Related Formulae (INTEGRATION DECOMPOSITON METHOD (TEXT<\/a>)<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{1cm}\\ \\color{red}{ii)\\  Evaluate:\\ \\hspace{2cm}\\ (i)\\ \\int\\ \\frac{sec^2(log x)}{ x}\\ dx\\ \\hspace{2cm}\\ (ii)\\ \\int \\frac{dx}{x^2 &#8211; 36}}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/12\/4-2-integration-by-substitution\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/12\/4-2-integration-by-substitution\/\">Refer Example 7 under Integration By Substitution<\/a><\/p>\n\n\n\n<p>         <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/16\/4-3-standard-integrals\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/16\/4-3-standard-integrals\/\">Refer Example No. 2 (STANDARD INTEGRALS)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[15.\\ \\color{red}{i)\\ Evaluate:\\ \\hspace{2cm}\\ (i)\\ \\int x\\ sin\\ 2x\\ dx\\ \\hspace{2cm}\\ (ii)\\ \\int x^2\\ sin\\ 2x\\ dx}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/5-1-integration-by-parts\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/5-1-integration-by-parts\/\">Refer Example No. 5 INTEGRATION BY PARTS<\/a><\/p>\n\n\n\n<p>          <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/bernoulllis-formula\/\" data-type=\"URL\" data-id=\"https:\/\/yanamtakshashila.com\/2021\/04\/18\/bernoulllis-formula\/\">Refer Example No. 2 (BERNOULLI&#8217;S FORMULA)<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{1cm}\\ ii.\\ \\color{red}{Evaluate: \\int_0^\\frac{\\pi}{2} (2 + sin x)^3 cos x \\ dx}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<p>Soln: <a href=\"https:\/\/yanamtakshashila.com\/2021\/04\/21\/definite-integrals\/\">Refer Example No. 9 DEFINITE INTEGRALS<\/a><\/p>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<!-- Leader board 1 -->\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:728px;height:90px\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"8769628924\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Soln: Refer Example 1 under Integration Decomposition Method Soln: Refer Example 3 under Integration By Substitution Soln: Refer Example No. 1 (STANDARD INTEGRALS) Soln: Refer Example No. 1 INTEGRATION BY PARTS Soln: Refer Example No. 1 (BERNOULLI&#8217;S FORMULA) Soln: Refer Example No. 1 DEFINITE INTEGRALS Soln: Refer Example 6 under Integration Decomposition Method Soln: Refer [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":0,"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":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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