Draw a rough sketch of the given curve $y=1+|x+1|, x=-3, x=3$, $y=0$ and find the area of the region bounded by them, using integration.
We have, $y=1+|x+1|, x=-3, x=3$ and $y=0$
$\because\quad y=\left\{\begin{array}{cc}-x, & \text { if } x<-1 \\ x+2, & \text { if } x \geq-1\end{array}\right.$
$$\begin{aligned} \therefore \quad \text { Area of shaded region, } A & =\int_{-3}^{-1}-x d x+\int_{-1}^3(x+2) d x \\ & =-\left[\frac{x^2}{2}\right]_{-3}^{-1}+\left[\frac{x^2}{2}+2 x\right]_{-1}^3 \\ & =-\left[\frac{1}{2}-\frac{9}{2}\right]+\left[\frac{9}{2}+6-\frac{1}{2}+2\right] \\ & =-[-4]+[8+4] \\ & =12+4=16 \text { sq units } \end{aligned}$$
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