I need to draw the graph of the area $D$ covered by the two curves and then find the actual value using a multiple integral listed above. The parameters are: $$C: x=3\cos(t), y=2\sin(t) ,(0\leqslant t \leqslant 2\pi) $$
Using the Jacobian functions $x$ becomes $x=3r\cos(\theta )$ and $y$ becomes $y=2r\sin(\theta )$. In addition, the area $D$ moves to $E: 0\leqslant r \leqslant 1, 0\leqslant \theta \leqslant 2\pi $(according to the answers). How does the range of $r$ become $0⩽r⩽1$ if we get an ellipse?