MCQ
$\int_0^{\pi /2} {\sqrt {\cos \theta } {{\sin }^3}\theta } \,d\theta = $
- A$\frac{{20}}{{21}}$
- ✓$\frac{8}{{21}}$
- C$\frac{{ - 20}}{{21}}$
- D$\frac{{ - 8}}{{21}}$
Put $t = \cos \theta \Rightarrow dt = - \sin \theta \,\,d\theta ,$ then
$I =$$ - \int_1^0 {{t^{1/2}}(1 - {t^2})dt = \int_0^1 {({t^{1/2}} - {t^{5/2}})} } $$dt$
$I = $$\left[ {\frac{2}{3}{t^{3/2}} - \frac{2}{7}{t^{7/2}}} \right]_0^1 = \frac{8}{{21}}$.
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