Question

Area lying in the first quadrant and bounded by the circle `x^2+y^2=4`and the lines `x= 0 a n dx= 2`is(A) `pi` (B) `pi/2` (C) `pi/3` (D) `pi/4`
A. `pi`
B. `(pi)/(2)`
C. `(pi)/(3)`
D. `(pi)/(4)`

Answer 1

Correct Answer - 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.