Constrained Integral

• May 22nd 2008, 03:46 AM
chogo
Constrained Integral
I have a difficult integral to solve. I can do it numerically, except i have two rigid constraints on the integral bounds

Can someone suggest reading ares on either how to numerically solve this or analytically.

thanks

sam
• May 22nd 2008, 03:50 AM
mr fantastic
Quote:

Originally Posted by chogo
I have a difficult integral to solve. I can do it numerically, except i have two rigid constraints on the integral bounds

Can someone suggest reading ares on either how to numerically solve this or analytically.

thanks

sam

At the moment there's a third constraint making it impossible to give an answer: There's no integral ......
• May 22nd 2008, 04:16 AM
chogo
$\displaystyle P(u<T_1<v | O_1,...,O_k,N) = A \int_u^v \int T_1^{O_1} \prod_{i=2}^k T_i^{O_i}$

k={1,2,3 or 4}

0<O<N

A is a constant

------- The bounds constraints for the second integral are

$\displaystyle \sum_{j=2}^k T_i \in [1-v,1-u]$

and

$\displaystyle 0 \leq T_i \leq 1 ~~ \forall = 2,...,k$
• May 22nd 2008, 05:07 AM
chogo
is that enough information?