# Integral of a product

• Jan 15th 2007, 03:24 AM
chogo
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
• Jan 15th 2007, 03:29 AM
chogo
i forgot to add the integral is taken from u to v

and the product from 1 to k
• Jan 15th 2007, 05:19 AM
CaptainBlack
Quote:

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
• Jan 15th 2007, 06:02 AM
chogo
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?
• Jan 23rd 2007, 02:01 AM
chogo
so does anyone know how to solve this integral? or should i just implement simpsons rule for an aproximate solution?
• Jan 23rd 2007, 02:56 AM
CaptainBlack
Quote:

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