Evaluate $\int ...\int_{R_n}dV_n(x_1^2 + x_2^2 + ... + x_n^2)$ , where $n$ and $R_n$ is defined in the body of this question.

Hello. I am confused about how to solve the following integral. I see that $n$ is a natural number so my initial thought was to find some sort of recurrence relation which yields the $n^{th}$ integral, but I'm unsure. Can somebody help me?

Let n be a positive integer. Evaluate $\int ...\int_{R_n}dV_n(x_1^2 + x_2^2 + ... + x_n^2)$ , where $R_n = \{(x_1,x_2,...,x_n) \in \mathcal{R}^n : 0 \leq x_i \leq 1, 1 \leq i \leq n\}$.


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