Giá trị của tích phân \(I=\int\limits_{0}^{\frac{\...

A

- Hướng dẫn giải

\(\begin{array}{l} I=\int\limits_{0}^{\frac{\pi}{2}} \cos ^{4} x \sin ^{2} x d x=\frac{1}{4} \int\limits_{0}^{\frac{\pi}{2}} \cos ^{2} x \sin ^{2} 2 x d x=\frac{1}{16} \int\limits_{0}^{\frac{\pi}{2}}(1-\cos 4 x) d x+\frac{1}{4} \int\limits_{0}^{\frac{\pi}{2}} \cos 2 x \sin ^{2} 2 x d x \\ =\left.\left(\frac{x}{16}-\frac{1}{64} \sin 4 x+\frac{\sin ^{3} 2 x}{24}\right)\right|_{0} ^{\frac{\pi}{2}}=\frac{\pi}{32} \end{array}\)