Question

Help...!!!

Convert the following question into Beta function.

Answer 1

\[\int\limits_{0}^{1}x^{4}(1-\sqrt{x})^6dx\]

Answer 2

substitute \(x = u^2 \implies dx = 2u\,du\)
\[\int\limits_0^1 (u^2)^4(1-u)^6 2udu =2\int\limits_0^1 u^9(1-u)^6 du = 2B(10,7) \]

Answer 3

thank you so much @rational

Answer 4

yw