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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 area bounded by the circle and the lines, `x=0` and `x=2`, in the first quadrant is represented as shaded region in the plot.
Area of `triangleOAB=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`
`= 2(pi/2)` = `pi` sq. units
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