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Draw a rough sketch of the given curve y...

Draw a rough sketch of the given curve `y=1+abs(x+1),x=-3, x=3, y=0` and find the area of the region bounded by them, using integration.

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We have `y=1+|x+1|,`,x=-3,x =3 ,x=3 and y =0

`therefore y={:{(-x, if x lt-1),(x+2, ifx ge -1):}`
`therefore "Area of shaded refion" ,A =int _(-3)^(-1) -x dx + int _(-1)^(3)(x+2)dx`
`=-[(x^(2))/(2)]^(-1)+[(x^(2))/(2)+2x]_(-1)^(3)`
`-=[1/2-9/2]+[9/2+6-1/2+]`
`=- [-4]+[8+4]`
=12+4 = 16 sq units
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