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$\int_0^{\pi / 2} \sin ^2 x \cos ^3 x d x=$
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Verified Answer
The correct answer is:
$\frac{2}{15}$
Using gamma function,
$\int_0^{\pi / 2} \sin ^2 x \cos ^3 x d x=\frac{\Gamma\left(\frac{3}{2}\right) \Gamma 2}{2 \Gamma\left(\frac{7}{2}\right)}=\frac{2}{15}$
$\int_0^{\pi / 2} \sin ^2 x \cos ^3 x d x=\frac{\Gamma\left(\frac{3}{2}\right) \Gamma 2}{2 \Gamma\left(\frac{7}{2}\right)}=\frac{2}{15}$
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