MIT Integration Question:
Find: $$\int_{0}^{4} \begin{pmatrix} x \\ 5\end{pmatrix} dx$$
I know this might be somewhat simplified using the Gamma Function, however is there any simpler way to find this integral?
2026-04-03 21:02:46.1775250166
Integral of Choose functions
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Just use the definition of the generalized binomial coefficient: $$\int_{0}^{4}\binom{x}{5}dx =\frac{1}{5!}\int_{0}^{4}x\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)dx=0$$