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Sketch the region bounded by the curves y = x2 + 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 = 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