# Integral Calculation

1. Aug 3, 2004

### kprokopi

I am trying to calculate (analytically) the integral:
$\int_{0}^{\pi} \left [ \frac{ \sin( \frac{k_0 W \cos \theta}{2})}{\cos \theta} \right]^2 J_{0}(k_0 L \sin \theta ) \sin^3 (\theta ) d \theta$
where $k_0, W, L$ are constants and $J_0$ is the Bessel function of the first kind of order zero.

Hint: Maybe we can use sine integrals $Si(x)=\int_{0}^{x} \frac{\sin(\tau)}{\tau} d \tau$.

kprokopi

2. Aug 3, 2004

### arildno

Eeh, you don't happen to be a masochist or something ()??

Use Mathematica and see what it spits out.

3. Aug 3, 2004

### KnowledgeIsPower

That looks tricky.
Can't you cheat and use the trapezium rule with a large number of intervals? -_-;;

4. Aug 5, 2004

### Gza

Just try typing that monster into mathematica :rofl: