(a) Evaluate $\displaystyle \int _c\,\!\displaystyle \frac{-ydx+xdy}{4x^2+25y^2} $ when C is the ellipse $\displaystyle \displaystyle \frac{x^2}{25}+\displaystyle \frac{y^2}{4}=1$, taken counter-clockwise.

(b) If C' is the square with vertices (+-11,0),(0,+-11), taken counter-clockwise, why can we not use Green's theorem directly to calculate the integral along C'?

Use Green's theorem and part (a) to evaluate thei ntegral.