Tính tích phân I = intlimits_0fracpi 2 xcos xdx .

Đặt $\left\{ \begin{array}{l}
u = x\\
dv = \cos xdx
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
du = dx\\
v = \sin x
\end{array} \right.$
$I = \left. {\left( {x\sin x} \right)} \right|_0^{\pi /2} - \int\limits_0^{\pi /2} {\sin xdx} = \frac{\pi }{2} + \left. {\left( {\cos x} \right)} \right|_0^{\pi /2} = \frac{\pi }{2} - 1.$