Could anyone help me with this problem. I really cant see how I can tackle solving it? I think the result is to be expressed with Gamma function.
If $V\subset\mathbb{R}^n$ is bounded by the coordinate planes $x_i=0$ and the surface: $(\frac{x_1}{a_1})^{p_1}+(\frac{x_2}{a_2})^{p_2}+...+(\frac{x_n}{a_n})^{p_n}=1$, then compute the integral: $$\idotsint _V\prod_{i=1}^{n}x_i^{a_i-1}d^nx$$