<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>1.	(a) Find the integral of\(\int{\frac{x}{\sqrt{1-{{x}^{2}}}}}\text{ d}x\).<br>	    (b) Hence, find the exact value of \(\int\limits_{0}^{\frac{1}{2}}{\frac{{{x}^{3}}}{\sqrt{1-{{x}^{2}}}}\text{ d}x}\).<br>2.	Find\(\int{\frac{2+\cos x}{{{\sin }^{2}}x}}\text{ d}x\).<br>3.	Find \(\int{\sin x(1+{{\cos }^{2}}x)}\text{ d}x\)<br>4.	Integrate \(\int{{{x}^{2}}\cos 2x}\text{ d}x\)<br>5.	Show that&nbsp;\(\int\limits_{0}^{\frac{\pi }{4}}{x{{\tan }^{2}}x\text{ d}x}=\frac{\pi }{32}(8-\pi )-\ln \sqrt{2}\)<br>6.	Find \(\int{\frac{\sin \theta \cos \theta }{{{(3+5{{\sin }^{2}}\theta -2{{\cos }^{2}}\theta )}^{\frac{1}{3}}}}}\text{ d}\theta \)<br>7.	Show that&nbsp;\(\int\limits_{0}^{\frac{\pi }{4}}{{{(1-\tan x)}^{2}}\text{ d}x}=1-\ln 2\)<br>8.	\(\int{\frac{2x+1}{\sqrt{x+1}}}\text{ d}x\)<br><br></p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><p>9.	Find \(\int{\frac{x-7}{2{{x}^{2}}-3x-2}}\text{ d}x\)<br>10.	Find\(\int\limits_{0}^{\frac{\pi }{3}}{{{\sin }^{3}}x\text{ d}x}\)<br>11.	Evaluate \(\int\limits_{0}^{\frac{\pi }{4}}{\sin 3x\sin x\text{ d}x}\)<br>12.	Find \(\int{{{\sin }^{2}}\theta {{\cos }^{3}}\theta }\text{ d}\theta \)<br>13.	Find \(\int{\cos e{{c}^{2}}\theta \sqrt{\cot \theta }}\text{ d}\theta \)<br>14.	Integrate \(\int{{{\cos }^{2}}\theta }(\sin \theta +\sec \theta \text{cosec }\theta )\text{ d}\theta \)<br>15.	Find \(\int{{{\sin }^{3}}\theta {{\cos }^{2}}\theta }\text{ d}\theta \)<br>16.	\(\int{\sqrt{{{x}^{2}}-5}}\text{ d}x\)<br>17.	\(\int{{{3}^{\sqrt{2x+1}}}}\text{ d}x\)<br>18.	\(\int{\frac{x{{\sin }^{-1}}({{x}^{2}})}{\sqrt{1-{{x}^{4}}}}}\text{ d}x\) <br></p></div></div></div>

Integration by Substitution

Techniques of  Integration

H2 Math

International Baccalaureate Higher Level Mathematics

Techniques of Integration - Integration by Substitution

Question ba06a134