Re: Solving an integral

C6L1V@xxxxxxx wrote:

Jens Benecke wrote:
Hi everybody,

I am trying to solve this integral:
f := int ( cos(x) / sqrt[ A*A*sin(x/2)*sin(x/2) + (Bx)^2] dx,
x=0..N*2*pi (...)
Thank you! :)

Second: Your integrand seems to have a 1/x singularity around x=0.
Hence your integral does not converge.

Ah. Here come the engineers :-) This integral represents (read: is
proportional to) a physical measure (in fact, an inductivity) and
therefore *should* converge. Somehow. Remembering my calculus classes in
university, I seem to recall that a singularity does not *necessarily*
imply that integration diverges. (Right?)

Not necessarily, but it depends on the type of singularity. In your
case, the integral diverges---no question. As for needing to converge

Hello,

Would the integral also diverge if I left the (Bx)^2 part out?
Because for that integral, I have a (finite) solution. I have tried to
transfer this solution to my problem but haven't yet been successful.

because it is a physical quantity, well, that argument does not apply.
In classical physics (and in quantum field theory too) there are
numerous physical quantities represented by divergent
integrals---usually because either classical physics breaks down in
some appropriate domain, or because some type of approximation was used
way outside its region of validity. Also, as you say, you might have
made an error. (That would be my guess.)

I hope so, because that would mean that it's not impossible. :-)

I have published a short description about how I came to this formula here:
www.jensbenecke.de/temp/, induction-orig.pdf (calculation of the induction
of a torus) and indcution-jens.pdf (my attempt at extending it to a coil).

Maybe you would like to have a look. The explanations are in German (in my
paper) but the math is international. :-)


R.G. Vickson
Adjunct Professor, University of Waterloo

Thank you for your help!


--
Jens Benecke
.

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