Find the value of Line Integral $\int_{C}F.dr$ where $\vec{F} = (x + y)\hat{i} + (1-x)\hat{j}$ where $C$ is the portion of the curve $x^2/4 + y^2/9 = 1$ that is in 4th quadrant with anti clockwise notation.
Now, using Green's theorem this Line integral is
$\displaystyle \int \int -2 dx dy$ , Since ellipse is symmetric in all quadrants, area in 4th quadrant = 1/4 area of ellipse,
This gives me $-3\pi$
However, the answer given to me is $5 - 3\pi$
Can anyone tell me the error in my solution ?
Thank you.