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The parabola y^(2)=4x+1 divides the disc...

The parabola `y^(2)=4x+1` divides the disc `x^(2)+y^(2) le 1` into two regions with areas `A_(1)` and `A_(2)`. Then `|A_(1)-A_(2)|` equal

A

`1/3`

B

`2/3`

C

`(pi)/(4)`

D

`(pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`A_(1)=2 int_(-1//4)^(0)sqrt(4x+1)dx+2int_(0)^(1)sqrt(1-x^(2))dx`

Solve `A_(1)=(1)/(3)+(pi)/(2)`
`A_(2)=pi(1)^(2)-A_(1)=(pi)/(2)-(1)/(3)`
`|A_(1)-A_(2)|=(2)/(3)`
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