Tích phân \(I=\int_{0}^{\frac{\pi}{2}} \cos ^{2} x...

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- Hướng dẫn giải

\(\begin{aligned} I &=\int_{0}^{\frac{\pi}{2}} \cos ^{2} x \cos 2 x d x=\frac{1}{2} \int_{0}^{\frac{\pi}{2}}(1+\cos 2 x) \cos 2 x d x=\frac{1}{4} \int_{0}^{\frac{\pi}{2}}(1+2 \cos 2 x+\cos 4 x) d x \\ &=\left.\frac{1}{4}\left(x+\sin 2 x+\frac{1}{4} \sin 4 x\right)\right|_{0} ^{\frac{\pi}{2}}=\frac{\pi}{8} \end{aligned}\)