Đáp án:
Giải thích các bước giải:
Đặt:
\(\begin{array}{l}
\left\{ \begin{array}{l}
u = mx\\
dv = \cos xdx
\end{array} \right. \to \left\{ \begin{array}{l}
du = mdx\\
v = \sin x
\end{array} \right.\\
\to \int\limits_0^\pi {\left| {mx\cos x} \right|dx} = \int\limits_0^{\frac{\pi }{2}} {mx\cos xdx - \int\limits_{\frac{\pi }{2}}^0 {mx\cos xdx} } \\
= mx.\sin x\left| {_0^{\frac{\pi }{2}}} \right. - m\int\limits_0^{\frac{\pi }{2}} {\sin xdx} - mx.\sin x\left| {_{\frac{\pi }{2}}^\pi } \right. + m\int\limits_{\frac{\pi }{2}}^\pi {\sin xdx} \\
= m.\frac{\pi }{2} + m.\cos x\left| {_0^{\frac{\pi }{2}}} \right. + m.\frac{\pi }{2} - m.\cos x\left| {_{\frac{\pi }{2}}^\pi } \right.\\
= m\pi - m + m = m\pi = 3\pi \\
\to m = 3
\end{array}\)
