I'm learning about integration on manifolds in my Calculus II course. I have a lot of trouble with it and now I'm posed with the following question:
Evaluatie $\int_{Q} b \text{ d}\textbf{x}$ over the hypersurface $Q=\{\textbf{x}\in\mathbb{R}^{n} : x_{i} \geq 0, 1 \leq i \leq n, x_{1}+x_{2}+...+x_{n} \leq k\}$.
I honestly have no idea where to even start. I thought of extracting all the integrals, somewhat like this: $b\int_{0}^{1} \text{ d}\textbf{x}_{1}+b\int_{0}^{1} \text{ d}_{2}\textbf{x}+...$.
But the answers I can choose from are like $bk^{n}(n-1)!$, $\frac{bk^{n}}{(n-1)!}$, $bk^{n-1}(n)!$ or $\frac{bk^{n-1}}{(n-1)!}$ and so on, a lot of variations on these examples.
Again, like you probably already notice I'm pretty clueless so any help would be much appreciated.
Thanks.