Evaluate the following integrals \[ \int_{0}^{\pi / 4}\left(a^{2} \cos ^{2} x+b^{2} \sin ^{2} x\...

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Evaluate the following integrals
\[
\int_{0}^{\pi / 4}\left(a^{2} \cos ^{2} x+b^{2} \sin ^{2} x\right) d x
\]
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