Sketch the region `{(x, 0):y=sqrt(4-x^(2))}` and X-axis. Find the area of the region using integration.

Answer

N/a

Explanation

Given region is `{(x, 0):y=sqrt(4-x^(2))}` and X-axis.
We have, `y=sqrt(4-x^(2))rArry^(2)=4-x^(2)rArrx^(2)+y^(2)=4`

`:." Area of shaded region, "A=int_(-2)^(2)sqrt(4-x^(2))dx=int_(-2)^(2)sqrt(2^(2)-x^(2))dx`
`=[x/2sqrt(2^(2)-x^(2))+(2^(2))/2 .sin^(-1)(x)/2]_(-2)^(2)`
`=2/2 .0+0. pi/2+2/2 .0-2sin^(-1)(-1)=2. pi/2+2. pi/2`
`=2pi" sq units"`