How to use the parameterization to find volume of ellipsoid?

Question

If I have the ellipse in $\mathbb{R}^2$ to be defined as $x^2+4y^2=1$ with the parameterization $\gamma: \mathbb{R}^1 \rightarrow \mathbb{R}^2$ defined as $\gamma(t)=cos(t),4sin(t)$ how would I set up an integral to solve for the volume of my ellipsoid?