$(1$ point$)$

A$)$

Use Green's theorem to compute the area inside the ellipse $\frac{x^2}{{14}^2}+\frac{y^2}{3^2}=1.$

Use the fact that the area can be written as

${}_{D}dxdy=\frac{1}{2}{\displaystyle \underset{\text{d}\text{e}\text{l}\text{D}}{\overset{\phantom{}}{}}}-ydx+xdy$

Hint: $x(t)=14cos(t).$

The area is

B$)$

Find a parametrization of the curve $x^{\frac{2}{3}}+y^{\frac{2}{3}}=6^{\frac{2}{3}}$ and use it to compute the area of the interior.

Hint: $x(t)=6co{s}^3(t).$