Lời giải:Ta có \(mx.\sin x = 0 \Leftrightarrow x = 0\,\,\)
\(S = \int\limits_{ - \,\frac{\pi }{2}}^{\frac{\pi }{2}} {\left| {\,m{\rm{x}}.\sin \,x\,} \right|dx = \left| {\int\limits_{ - \,\frac{\pi }{2}}^0 {m{\rm{x}}.\sin \,x{\rm{dx}}\,} } \right|} + \left| {\int\limits_0^{\frac{\pi }{2}} {m{\rm{x}}.\sin \,x{\rm{dx}}\,} } \right|\)
\( = \left| {\,(\sin \,x - x.co\,s{\rm{x}})\left| \begin{array}{l}
0\\
- \,\frac{\pi }{2}
\end{array} \right.\,\,} \right| + \left| {\,(\sin \,x - x.co\,s{\rm{x}})\left| \begin{array}{l}
\frac{\pi }{2}\\
0
\end{array} \right.\,\,} \right| = 2\left| {\,m\,} \right| \Rightarrow S = 4 \Leftrightarrow m = \pm 2\)
