Sketch the region bounded by the curves y = x^{2} + 2, y = x, x = 0 and x = 1. Also, find the area of the region.

To find area bounded x = 0, x = 1

And y = x ...(i)

y = x^{2} + 2 ...(ii)

Putting x = 1 in equation (ii) we get,

Y = 1 + 2 = 3

Putting x = 1 in equation (i) we get,

Y = 1

So the point of intersection B (1,3), A(1,1)

Equation (i) is a line passing through (1,1) and (0, 0)

Equation (2) is a parabola upward with vertex at (0, 2).

These are shown in the graph below: -

Required area = Region OABCO

The area of the region bounded by the curves y = x^{2} + 2, y = x, x = 0 and x = 1is

31