Problem #1

We have two polar curves r=2a(cos(theta/2))^2 and r=2a(sin(theta/2))^2 with a>0. We have to find the area of the potion of the plane they have in common.

For this problem, I've already sketch and I found the area=3a^2pi/2 but I'm not quite confident with my answer.

Problem # 2

Let's consider the curve with equation 3ay^2=x(a-x)^2 with a>0 . I want to find the area of the surface generated by rotating the loop of the curve about the x axis and y-axis.