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Area lying in the first quadrant and bou...

Area lying in the first quadrant and bounded by the circle `x^2+y^2=4`and the lines `x= 0` and `x= 2` is

A

`pi`

B

`(pi)/(2)`

C

`(pi)/(3)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
The region bounded by the circle and lines `x=0` and `x=2` in first quadrant is shown by shaded region in the figure.

` :. "Required area" =int_(0)^(2)ydx=int_(0)^(2)sqrt(4-x^(2))dx`
` [(x)/(2)sqrt(4-x^(2))+(4)/(2)"sin"^(-1)((x)/(2))]_(0)^(2)`
`=0+2sin^(-1)(1)-0`
`=2xx(pi)/(2)=pi` sq. units.
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