Hi. I wanted to know if I did this right:

Using double integrals, set in polar coordinates, the integral that gives the area for the region

From the picture:

The pink region represents the area I want.

The intersection is given for x=3/2, where:

Then

Tita 1 represents the limit on the angle for the circle that isn't centered at the origin. Is the limit for the brown region.

This is the limit on the angle for the orange region, for the circle centered at the origin.

Finally

With

Then

And the area:

The first integral represents the entire circle, the second the brown region and the third the orange region, both multiplied on two by simmetry