It can be shown that the line integral of F = xj around a closed curve in the xy - plane, oriented as in Green's Theorem, measures the area of the region enclosed by the curve. (You should verify this.)
Use this result to calculate the area within the region of the parameterized curve given below.
x = acos(t) y= bsin(t) for 0<t<2pi
The Attempt at a Solution
I tried integrating an ellipse using cartesian limits, but ended up with zero under a radical. I can't think of a way to integrate this in terms of t, since our book has no such example. Using Green's theorem does not put the a and b constants anywhere in the equation, which confuses me...