A) 4
B) 9
C) 2
D) \[\frac{9}{2}\]
Correct Answer: B
Solution :
[b] We have \[\left| x \right|+\left| x-1 \right|=\left\{ \begin{matrix} -x-(x-1)=-2x+1,if\,\,x\le 0 \\ x-(x-1)=1,if0\le x\le 1 \\ x+x-1=2x-1,ifx\ge 1 \\ \end{matrix} \right.\] \[{{I}_{1}}=\int\limits_{-2n-1}^{-2n}{{{\sin }^{27}}xdx=\int\limits_{2n+1}^{2n}{{{\sin }^{27}}(-x)(-dx)}}\]\[\therefore \int\limits_{-1}^{3}{(\left| x \right|+\left| x-1 \right|)dx}\] \[=\int_{-1}^{0}{(-2x+1)dx+\int_{0}^{1}{1dx+\int_{1}^{3}{(2x-1)dx}}}\] \[=\left[ -{{x}^{2}}+x \right]_{-1}^{0}+[x]_{0}^{1}+\left[ {{x}^{2}}-x \right]_{1}^{3}=9\]
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