Use Green's theorem in the plane to evaluate the work integral
W = ∫c F. dr = ∫ (3x – y)dx + (x + 2y) dy
where C is the boundry of the ellipse x+2 + 4y^2 = 9
Where exactly are you stuck?
Note that the given ellipse can be re-written as $\displaystyle \frac{x^2}{3^2} + \frac{y^2}{(3/2)^2} = 1$ so a = 3 and b = 3/2. And you know that the area of an ellipse with major and minor axes 2a and 2b is $\displaystyle \pi a b$, right .....?