# Region of ellipse and greens theorem

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?

• green is Green: always use a Capital for names. – Jean Marie Mar 22 '17 at 22:36

Your ellipse is $$\left( \frac{x}{2}\right)^2+\left(\frac{y}{1}\right)^2 =1$$ with $a=2$ and $b=1$ and has area $\pi a b= 2 \pi$