Question

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


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Answer 1

Answer:

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Answer 2

Answer:

The given curves are y=x

2

and y

2

=x i.e. y=

x

To find the intersection point of two curves, let us have

x

2

=

x

⟹x

4

=x

⟹x

4

−x=0

⟹x(x

3

−1)=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 =∫

0

1

(x

2

−

x

)dx

=

∣

∣

∣

∣

∣

∣

3

x

3

−

2

3

(x)

2

3

∣

∣

∣

∣

∣

∣

0

1

=

3

1

−

3

2

=−

3

1

Hence, area bounded by two parabolas y=x

2

and y

2

=x is −

3

1

.