The area of the region by the circle `x^(2)+y^(2)=1` is

Options

A. `2pi" sq units"`
B. `pi^(2)" sq units"`
C. `3pi^(2)" sq units"`
D. `4 pi " sq units"`

Answer

B

Explanation

We have, `x^(2)+y^(2)=1^(2) [ :'r=pm1]`
`rArr y^(2)=1^(2)-x^(2)rArry=sqrt(1-x^(2))`

`:." Area enclosed by circle "=int_(-1)^(1)sqrt(1^(2)-x^(2))dx=2.2int_(0)^(1)sqrt(1^(2)-x^(2))dx`
`=2.2[x/2sqrt(1^(2)-x^(2))+1^(2)/2sin^(-1). x/1]_(0)^(1)`
`=4[1/2 .0+1/2 . pi/2-0-1/2 .0]`
`=4. pi/4=pi " sq units"`