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.

Given;

Curve y = 1 + |x +1|, x = –3, x = 3, y = 0.

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Required area

= 4 + 12 = 16 sq.units