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## Homework Statement

So the problem asks to evaluate the integral along a contour of the function (e^x)*cos(y)*dx-(e^x)*sin(y)*dy, where the contour C is a broken line from A = (ln(2),0) to D = (0,1) to B = (-ln(2),0).

## Homework Equations

I know that the theorem states that the integral of a vector field dotted into a small portion dl of the contour is equal to the double integral of the the normal component (in this case the z component) of the curl of the vector field. So ∫V(dot)dl over a closed contour = ∫∫(partial with respect to x of the y-component of the vector field - partial with respect to y of the x-component of the vector field)dσ over the area σ.

## The Attempt at a Solution

I get stuck once I try to convert the single integral to the double integral. I know that if I connect B to A, I can make a closed contour, which was what I intended to integrate over. So I'm thinking I should try to evaluate the contour but I don't know how to go between x and y in order to do this. At first I wanted to convert to the double integral form in order to evaluate this, however when I do so I get that -e^x*sin(y)-(e^x*-cos(y)) = 0 which I don't think I should get. Am I computing something incorrectly? Am I just thinking about this incorrectly? Do I not want to take the partial of -e^x*sin(y) with respect to x minus the partial with respect to y of e^x*cos(y)?

Any help at all would be greatly appreciated. And this might go without saying, but I am going to say it anyways just in case: Please, please please DON'T tell me how to solve this problem, just what I am doing incorrectly. I really want to figure this out on my own. That isn't to say I don't appreciate any help, it's just that I want to understand this problem, not jut get the right answer.

Thank you