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The area of the region enclosed by ...

The area of the region enclosed by ` x ^ 2 + y ^ 2 = 2 , y ^ 2 = x ` and y - axis is

A

`(pi)/4+1/3`

B

`(pi)/2+1/3`

C

`(pi)/4-1/3`

D

`(pi)/2-1/3`

Text Solution

Verified by Experts

The correct Answer is:
D
`x^2+y^2=2 , y^2=x`
Area=2 `int_0^1 y^2dy+2 int_0^sqrt2 sqrt(2-y^2)dy`
`=[2/3 y^3]_0^1 +[ ysqrt(2-y^2)+2 sin^(-1) y/sqrt2]_1^sqrt2`
`=2/3 + [pi-(1+pi/2)]=pi/2-1/3` Area = `pi/2 -1/3`
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