I have the integral
$\int_0^1 \cdots \int_0^1 e^{-w^Tx} dx$ that I want to integrate. The constraints are that $w^Tx = 1$ and $0\leq x \leq 1$ though I guess the latter is implied by the domain of integration anyway. $w, x$ are vectors. Is there a nice way to go about this problem?
Edit: Note that this is equivalent to integrating over the intersection of a simplex and a box if we take $t_i = w_ix_i$.
Thanks