# Thread: Integral of a product

1. ## Integral of a product

Hi im developing a method which uses are dirichlet distribution

I am however using a frequency range and so have to include an integral. I am however stuck trying to evaluate this integral. What confuses me is the product

\int \prod T^O dT

if anyone can help

2. i forgot to add the integral is taken from u to v

and the product from 1 to k

3. Originally Posted by chogo
Hi im developing a method which uses are dirichlet distribution

I am however using a frequency range and so have to include an integral. I am however stuck trying to evaluate this integral. What confuses me is the product

\int \prod T^O dT

if anyone can help
Do you mean:

$\displaystyle \int_u^v \prod_{i=1}^k T^{O_i}\ dT\ \ \ ?$

RonL

4. yes sorry i was given the wrong equation, the one you have written is correct

how do i evaluate that integral? is it anything tricky or is it just the trivial solution i think it is?

5. so does anyone know how to solve this integral? or should i just implement simpsons rule for an aproximate solution?

6. Originally Posted by chogo
so does anyone know how to solve this integral? or should i just implement simpsons rule for an aproximate solution?
Assuming $\displaystyle \sum_{i=1}^kO_i \ne -1$

$\displaystyle \int_u^v \prod_{i=1}^k T^{O_i}\ dT=\int_u^v T^ {\sum_{i=1}^kO_i}\ dT=\left. \frac{1}{(\sum_{i=1}^kO_i) +1}T^ {(\sum_{i=1}^kO_i)+1}\right|_{T=u}^v$

RonL