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The area (in sq units) of the region {(x...

The area (in sq units) of the region `{(x, y) : y^2 gt= 2x and x^2 + y^2 lt= 4x, x gt= 0, y gt= 0}` is

A

`pi-(8)/(3)`

B

`pi-(4sqrt(2))/(3)`

C

`(pi)/(2)-(2sqrt(2))/(3)`

D

`pi-(4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`y^(2)=2x and x^(2)+y^(2)=4x" meet at "O(0,0) and B(2,2) {(2,-2)" is not considered as "x,yge0}`

`"Now required area "=(1)/(4)pixx4-overset(2)underset(0)intsqrt(2x)dx`
`=pi-sqrt(2)(2)/(3)[x^(3//2)]_(0)^(2)`
`=pi-(8)/(3)`
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