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I am trying to solve a line integral:

Find the value of \int -2y dx + x^2 dy over the circle x^2 + y^2 = 9

as you can see, this is a line integral, and I am trying to figure a quick way how it should be solved.

I thought of converting coordinates to (sint,cost) which will end up as a trigonometric function which needs to be integrated, but I believe there is a much easier way which I am not sure about.

Also, I am not sure what is the notation f(y) dx + g(x) dy stands for.

Is it the same as [f(y) - i g(x)] dz?

Thanks for any help.