Tích phân \(I = \int\limits...

B

- Hướng dẫn giải

Đặt \(\left\{ \begin{array}{l}u = x\\dv = \cos xdx\end{array} \right. \Rightarrow \left\{ \begin{array}{l}du = dx\\v = \sin x\end{array} \right.\)

\(\begin{array}{l} \Rightarrow I = \left. {\left( {x\sin x} \right)} \right|_{\frac{\pi }{6}}^{\frac{\pi }{2}} - \int\limits_{\frac{\pi }{6}}^{\frac{\pi }{2}} {\sin xdx} \\ = \left. {\left( {x\sin x} \right)} \right|_{\frac{\pi }{6}}^{\frac{\pi }{2}} + \left. {\left( {\cos x} \right)} \right|_{\frac{\pi }{6}}^{\frac{\pi }{2}}\\ = \frac{{7\pi }}{{12}} - \frac{{\sqrt 3 }}{2}\end{array}\)