Let γ be the ellipse $x^2 + 4y^ 2 = 4$, oriented anticlockwise. Compute $\int_c(4y − 3x)dx + (x − 4y)dy$
I used green theorem with P and Q. and got $$-3\int\int_\ dxdy$$
The answer is $-6\pi,$ so how do I get $2\pi$ from the double integral? Or am I just tackling the problem all wrong?