A) \[\frac{3}{\pi }+\frac{2}{{{\pi }^{2}}}\]
B) \[\frac{3}{{{\pi }^{2}}}+\frac{1}{\pi }\]
C) \[\frac{3}{{{\pi }^{{}}}}+\frac{1}{{{\pi }^{2}}}\]
D) \[\frac{3}{{{\pi }^{{}}}}-\frac{1}{{{\pi }^{2}}}\]
Correct Answer: C
Solution :
\[\int\limits_{-1}^{3/2}{\left| x\sin \pi x \right|dx}\] |
\[For\,-1\le x<0\Rightarrow -\pi <px<0\] |
\[\Rightarrow \sin \,\pi x<0\] \[\Rightarrow x\sin \,\pi x>0\] |
For \[1<x<3/2\Rightarrow \pi <\pi x<3\pi /2\] |
\[\Rightarrow \sin \,\pi x<0\] \[\Rightarrow x\sin \,\pi x<0\] |
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