Q. 315.0( 2 Votes )

Sketch the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 1. Also, find the area of the region.

Answer :

To find area bounded x = 0, x = 1

And y = x ...(i)


y = x2 + 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 = x2 + 2, y = x, x = 0 and x = 1is


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