Question

Find the area of the region.?

Answer 1

`= (3 pi)/2`

Explanation:

`2 int_0^(pi/2) dx \ (3 cos x)/(1+ sin^2 x)`

let `z = sin x, qquad dz = cos x \ dx`

`=2 int_0^1 (dz)/cos x \ (3 cos x)/(1+ z^2)`

`=6 ( tan^(-1) z )_0^1 = (3 pi)/2`