<ol class="abc-list"><li><div class="list-item-paragraph">Use the substitution $x=\cos \theta $ to find the exact value of $\int_{\frac{\pi }{2}}^{\pi }{\frac{\sin \theta }{1+{{\cos }^{2}}\theta }}\,\,\mathrm{d}\theta $.</div><p style="text-align: right;">[5]</p></li><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-paragraph">Find $\int{{{\mathrm{e}}^{x}}\sin 2x\,\mathrm{d}x}$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-paragraph">Hence find the exact value of $5\int_{0}^{\frac{\pi }{2}}{{{\mathrm{e}}^{x\,}}\sin \,2x\,\mathrm{d}x}$.</div><p style="text-align: right;">[2]</p></li></ol></li></ol>

Use the substitution $x=\cos \theta $ to find the exact value of $\displaystyle\displaystyle \int_{\frac{\pi }{2}}^{\pi }{\frac{\sin \theta }{1+{{\cos }^{2}}\theta }}\,\,\mathrm{d}\theta $.

Techniques of  Integration - General

Techniques of  Integration

H2 Math

International Baccalaureate Higher Level Mathematics

2010 MI P1 Q11

2010 MI P1 Q11

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