Question

1.)Use a double integral to find the area of the region.

One loop of the rose

r = 4 cos 3θ

2.)Use a double integral to find the area of the region.

The region inside the circle

(x − 3)2 + y2 = 9

and outside the circle

x2 + y2 = 9

3.)Use polar coordinates to find the volume of the given solid.

Inside the sphere x2 + y2 + z2 = 16 and outside the cylinder x2 + y2 = 1