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By using the properties of definite integrals, evaluate the integrals
$\int_0^{\frac{\pi}{2}} \cos ^2 x d x=I($ say $)$
$\int_0^{\frac{\pi}{2}} \cos ^2 x d x=I($ say $)$
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$\begin{aligned} \mathrm{I} &=\frac{1}{2} \int_0^{\frac{\pi}{2}}(1+\cos 2 x) d x \\ &=\frac{1}{2}\left[x+\frac{\sin 2 x}{2}\right]_0^{\frac{\pi}{2}}=\frac{\pi}{4} . \end{aligned}$
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