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The area bounded by the curves y^2=4x an...

The area bounded by the curves `y^2=4x` and `x^2=4y`

A

0 sq units

B

`(32)/(3)` sq units

C

`(16)/(3)` sq units

D

`(8)/(3)` sq units

Text Solution

Verified by Experts

The correct Answer is:
C
For the point of inersection for `y^(2)=4x and x^(2)=4y`

`implies ((x^(2))/(4))^(2)=4x`
`implies x^(4)=4^(3)x`
`implies x=0,4`
`therefore` Area bounded between curves
`=int_(0)^(4)(sqrt(4x)-(x^(2))/(4))dx=[2.(x^(3//2))/((3)/(2))-(x^(3))/(12)]_(0)^(4)`
`=(4)/(3).(4)^(3//2)-((4)^(3))/(12)=(32)/(3)-(16)/(3)=(16)/(3)`
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