# Integral calculation

• Apr 16th 2009, 04:59 AM
hokutose
Integral calculation
Hi! I have a problem solving this integral.Could someone help me or give me an advice?

$\displaystyle$
$\displaystyle \int_{0}^{2\pi} cos(\theta)exp(a \cos(\theta))d\theta$

• Apr 16th 2009, 08:45 AM
Prove It
Quote:

Originally Posted by hokutose
Hi! I have a problem solving this integral.Could someone help me or give me an advice?

$\displaystyle$
$\displaystyle \int_{0}^{2\pi} cos(\theta)exp(a \cos(\theta))d\theta$

Are you sure you copied down the integral correctly?

Mathematica is telling me this can't be solved exactly...
• Apr 17th 2009, 12:22 AM
hokutose
Yes, i'm sure it's like that. I also tried with Mathematica,and it seems that there is no elemental solution,but for instance, the integral

$\displaystyle \int exp(\cos(a\theta))d\theta$
Can be expressed in terms of the modified bessel function of the first kind I0(x)
so i was wondering if i could do something like that...(my code is plenty of integrals so if i can avoid to compute any of them numerically it would be great)