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$\int_0^{\pi / 2} \cos ^2 x d x=$
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Verified Answer
The correct answer is:
$\frac{\pi}{4}$
Using gamma function,
$\int_0^{\pi / 2} \cos ^2 x d x=\frac{\Gamma\left(\frac{3}{2}\right) \Gamma\left(\frac{1}{2}\right)}{2 \Gamma(2)}=\frac{\frac{1}{2} \Gamma\left(\frac{1}{2}\right) \Gamma\left(\frac{1}{2}\right)}{2 \cdot 1 \cdot \Gamma(1)}=\frac{\pi}{4}$
$\int_0^{\pi / 2} \cos ^2 x d x=\frac{\Gamma\left(\frac{3}{2}\right) \Gamma\left(\frac{1}{2}\right)}{2 \Gamma(2)}=\frac{\frac{1}{2} \Gamma\left(\frac{1}{2}\right) \Gamma\left(\frac{1}{2}\right)}{2 \cdot 1 \cdot \Gamma(1)}=\frac{\pi}{4}$
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