Compute the area

Question

Compute the area contained within the curve $ (\frac{x}{5})^2 + (\frac{y}{4})^{2/3} =1$

I couldn't find which area the it is asking me to compute. I need a little help to find it

Answer 1

Alpha will plot it for you. The part above the $x$ axis is a hump, starting at $x=-5$, crossing the $y$ axis at $4$ and dropping back to the $x$ axis at $5$. I would integrate the region shown and double the result to account for the area below the axis. You have $$\left( \frac y4 \right)^{2/3}=1-\left( \frac x5 \right)^2\\\frac y4=\left(1-\left( \frac x5 \right)^2\right)^{3/2}\\y=4\left(1-\left( \frac x5 \right)^2\right)^{3/2}$$ to integrate