I am given a curve $C$ which is parametrized by:
$x(t)=Cos(t)$ and $y(t)=Sin(2t)$ for $-\frac{1}{2}\pi\leq t \leq \frac{1}{2}\pi$
Let $S$ be the surface you get if you revolve $C$ around the $y$-axis and let $V$ be the volume that is enclosed by surface $S$.
Let $F$ be the vector field that satisfies the following equation:
$\nabla\cdot F=1$.
I have to show that the volume $V$ is given by this double integral:
$\int \int_S F \cdot \hat N dS$.
I am having trouble getting started on this assignment. Using trigonometric identities I have rewritten the parametrization to:
$y=\sqrt{4x^2-4x^4}$
but other then that I am at a loss.
Thank you in advance for any help.