Find the Area:

Use a double integral to find the area of the region enclosed by both of the cardioids $r = 1 + \cos \theta$ and $ r = 1 - \cos \theta$.

Use double integration to find the area of the region in the $xy$-plane bounded by the given curves: $y = x, y = x^4$.

Use double integration to find the area of the circle with $r =1$. Yeah, you already know what this is, but convince yourself with math!

Find the area of the following region using double integrals: $x+y = 1, x+y = 2, 2x - 3y = 2$, and $2x - 3y = 5$.