Section 10.2: 1abcefgh, 4, 7

And:

1. Use Green's theorem to show that the area of a circle of radius $r$ is $\pi r^2$.

2. Use Green's theorem to find the area of the region $B$ enclosed by the hypocycloid $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$, where $a > 0$. Note: $\partial B$ may be parametrized by $\alpha(t) = (a\cos^3(t), a\sin^3(t))$, $0 \le t \le 2\pi$.

Answer : $\frac{3}{8}\pi a^2$