Hey, I'm trying to solve the following double line integral:

where and denote the line elements and the vector-valued function is given by

where denotes the Euclidean norm.

I tried various things: Assuming that with the help of the angle and the radius the line can be parametrized then the integral could be rewritten to

Since the function is zero when and get too large, this expression should be well defined. However, I'm having a hard time to find the correct integrations limits.

Also, I think that there might not exist an analytic expression for the double integral. If that's the case, I would be happy if I could do at least one analytic integration (and use for the other integral some numerical integration scheme).

Does anyone have an idea? Any comment is hightly appreciated!

Many thanks,

DeeAna