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Question

Find the area of the region bounded by the two parabolas y=x2 and y2=x.

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Solution

The given curves are y=x2 and y2=x i.e. y=x
To find the intersection point of two curves, let us have
x2=x
x4=x
x4x=0
x(x31)=0
x=0 and x=1
(0,0) and (1,1) are the points of intersection of two curves.
Area bounded by these two curves =10(x2x)dx
=∣ ∣x33(x)3232∣ ∣10
=1323=13
Hence, area bounded by two parabolas y=x2 and y2=x is 13.

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