Squashed ellipse

Calculus Level 3

Consider the curve defined by the parametric equations \[\begin{cases} x=a\sin \theta \\ y = a\sin^2 \theta \cos \theta \end{cases} \] for \(0 \le \theta \le 2\pi.\)

What is the area enclosed by the curve?

\(\)
Hint: Green’s theorem might help.

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