# Line Integrals

Evaluate
∫(x^2+arcsinx) dx + (arccosy)dy + (z^2+arctanz)dz
C
where C is parametrized by g(t)=(sint, cost, sin(2t)), 0<t<2pi

I tried doing it directly, but it gets really horrible and I don't think I can integrate the resulting function, is there a trick or short cut to this question?

Thank you!

## Answers and Replies

Calculate its rotational of the vectorial function, if its zero then try calculating the singularities inside C(where the function is infinite) Then isolate the singularities with circles with radius h with h going to zero. Evaluate the line integrals of those circles and there is your awnser. :)
If u get stuck check http://www.tubepolis.com [Broken]

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Are there any singularities? If we're doing it "directly", why does it matter whether there are singularities or not?

Will any theorem help?

HallsofIvy
Science Advisor
Homework Helper
That is a closed path and Stingray788 is simply referring to the fact that an exact differential over a close path is always 0. That is clearly an exact differential because the coefficient of dx depends only on x, the coefficient of dy depends only on y, the coefficient of dz depends only on z.