Question

Use the Gamma function to evaluate int_{0}{1)x^{4}{1-x}^{3}dx

Answer 1

$\int_{0}^1x^{4}(1-x)^{3}dx=\Beta(5,4)=\frac{\Gamma(5)\Gamma(4)}{\Gamma(9)}=\\ =\frac{4!\cdot 3!}{8!}=\frac{2\cdot3}{5\cdot 6\cdot 7\cdot8}=\frac{1}{280}$