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
$\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
$\displaystyle 0 \leq T_i \leq 1 ~~ \forall = 2,...,k$