A) \[\frac{{{x}^{2}}}{3}\]
B) \[-\frac{{{x}^{2}}}{3}\]
C) \[\frac{{{x}^{2}}|x|}{3}\]
D) None of these
Correct Answer: C
Solution :
Let \[I=\int{\underset{II}{\mathop{x}}\,|\underset{I}{\mathop{x}}\,|dx}\] \[=|x|\frac{{{x}^{2}}}{2}-\int{\frac{|x|}{x}}.\frac{{{x}^{2}}}{2}\,\,dx\] \[\Rightarrow \] \[I=\frac{{{x}^{2}}|x|}{2}-\frac{I}{2}\] \[\frac{3I}{2}=\frac{{{x}^{2}}|x|}{2}\] \[\Rightarrow \] \[I=\frac{{{x}^{2}}|x|}{3}\]
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