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

a) Use the fundamental theorem of line integrals to evaluate the line integral:

∫(2x/(x^2+y^2)^2)dx+(2y/(x^2+y^2)^2)dy (over C) Where C is the arc of the circle (x-4)^2+(y-5)^2=25 taken clockwise from (7,9) to (0,2). Explain why the fundamental theorem can be applied.

b) Obtain the same result by parameterizing the curve and evaluating the resulting integral

2. Relevant equations

fundamental theorem of line integrals :

∫(del)f * dr = f(r(b))-f(r(a))

3. The attempt at a solution

I'm supposed to find the function for which the function inside the integral is the gradient. I have:df/dx=(2x/(x^2+y^2)^2) =>> f=-(x^2+y^2)^-1 and df/dy=(2y/(x^2+y^2)^2) =>> f=-(x^2+y^2)^-1, so f(x,y)=-(x^2+y^2)^-1. As far as parameterizing the circle, I have x=5cost+4 and y=5sint+5. I'm completely stuck at this point. I don't see how to get values of t that yield those points on the circle, and I'm confused further because the circle is traversed in a clockwise direction. Any help would be appreciated, thanks.

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# Homework Help: Question involving fundamental theorem of line integrals

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