The curve $C$ with equation $x^{\frac{2}{3}}+y^{\frac{2}{3}}=5^{\frac{2}{3}}$ is parametrized by $x=5co{s}^3(t),y=5si{n}^3(t)$ for $0t2.$ Let $D$ be the region enclosed by this curve. From basic calculus, the area of $D$ is equal to ${\displaystyle \underset{-5}{\overset{5}{}}}dx,$ but this integral is hard to calcul?te$.$ Instead, use the expression

area$(D)=\frac{1}{2}{\displaystyle \underset{C}{\overset{\phantom{}}{}}}(xdy-ydx)$

to calculate the area of $D.$ The area of $D$ is $$