(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let C be the ellipse with center (0,0), major axis of length 2a, and minor axis of length 2b. Evaluate [tex]\oint_C xdy - ydx[/tex].

2. Relevant equations

I solved this two ways. First I parameterized x and y as [tex]x=a \cos \theta[/tex] and similarly for y. I also applied Green's theorem, which yielded [tex]\oint_C xdy - ydx = 2 \int \int_D dA[/tex] where D is the area enclosed by C (ie an ellipse.) In both cases I got the answer [tex]2\pi a b[/tex].

3. The attempt at a solution

My only question is, the book I am using says the answer is [tex]\frac{\pi a b}{2}[/tex]. This is an ETS book and they don't usually have typos, especially when it's the answer key to a previously administered exam. What am I missing?

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# Homework Help: Elliptic line integral

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