Let's circulate!

Calculus Level 5

Find the circulation \[\oint_{C}\frac{y}{x^2+y^2}dx-\frac{x}{x^2+y^2}dy\]

where \(C\) is the curve \(\frac{x^2}{9}+\frac{y^2}{4}=1\) with the counter-clockwise orientation.

If the answer is \(a\pi\), enter \(a\).

For a generalization, try this

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