A) \[0\]
B) \[2\]
C) \[4\]
D) \[-4\]
Correct Answer: D
Solution :
We know that, \[|x|=\left\{ \begin{matrix} -x, & if & x<0 \\ x, & if & x\ge 0 \\ \end{matrix} \right.\] \[\therefore \] \[\int_{-2}^{2}{(x-|x|)\,\,dx}\] \[=\int_{-2}^{0}{\{x-(x)\}dx+\int_{0}^{2}{(x-x)dx}}\] \[=\int_{-2}^{0}{2x\,\,dx+0}\] \[=2\left[ \frac{{{x}^{2}}}{2} \right]_{-2}^{0}\] \[=2\left[ 0-\frac{{{(-2)}^{2}}}{2} \right]=-4\]
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