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Area enclosed between the curves |y|=1-x...

Area enclosed between the curves `|y|=1-x^2` and `x^2+y^2=1` is (a) `(3pi-8)/3` (b) `(pi-8)/3` (c) `(2pi-8)/3` (d) None of these

A

`(3pi-8)/(3)` sq. units

B

`(pi-8)/(3)`

C

`(2pi-8)/(3)` sq. units

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A

The dotted area is
`A=int_(0)^(1)(1-x^(2))dx=(-(x^(3))/(3))_(0)^(1)=1-(1)/(3)=(2)/(3).`
Hence, area bounded by circle `x^(2)+y^(2)=1` and
`|y|=1-x^(2)`
=Lined area
=Area of circle - Area bounded by `|y|=1-x^(2)`
`=pi-4xx((2)/(3))=(3pi-8)/(3)` sq. units.
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