<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Find $\int{\frac{9}{\sqrt{3+2x-{{x}^{2}}}}}\mathrm{ d}x$. Hence, find the exact value of the constant $a$ for which $\int_{\ 0}^{\ 2}{\frac{9}{\sqrt{3+2x-{{x}^{2}}}}\mathrm{ d}x=\int_{\ -\tfrac{1}{2}}^{\ a}{\pi \left| \,1-2x\, \right|}}\mathrm{ d}x.$</div><p style="text-align: right;">[7]</p></li></ol>

Find $\displaystyle\displaystyle \int{\frac{9}{\sqrt{3+2x-{{x}^{2}}}}}\mathrm{ d}x$. Hence, find the exact value of the constant $a$ for which $\displaystyle\displaystyle \int_{\ 0}^{\ 2}{\frac{9}{\sqrt{3+2x-{{x}^{2}}}}\mathrm{ d}x=\displaystyle\displaystyle \int_{\ -\tfrac{1}{2}}^{\ a}{\pi \left| \,1-2x\, \right|}}\mathrm{ d}x.$

Techniques of  Integration - General

Techniques of  Integration

H2 Math

International Baccalaureate Higher Level Mathematics

2013 RI P1 Q12

2013 RI P1 Q12

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