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Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.

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Integrals I am curious about [closed]

Let $C_n(x) = \frac{n!}{\Gamma(x)\cdot \Gamma(n-x)}$ Is the following true: $\int_{0}^{n} [C_n(x)\cdot y^x \cdot (1-y)^{n-x}dx] = 1$?? just wondering In generality for continuous functions $f,g$ f …