A) \[-\frac{2}{35}\]
B) \[\frac{4}{35}\]
C) \[\frac{24}{35}\]
D) \[-\frac{8}{35}\]
Correct Answer: B
Solution :
\[\int_{0}^{1}{x}{{(1-x)}^{3/2}}dx\] \[={{\int_{0}^{1}{x}}^{(2-1)}}{{(1-x)}^{5/2-1}}dx\] \[=B(2,5/2)\left\{ \begin{matrix} \because B(m,n)-\int_{0}^{1}{{{x}^{m-1}}{{(1-x)}^{n-1}}dx} \\ \because B(m,n)=\frac{\Gamma m\Gamma n}{\Gamma (m+n)} \\ \end{matrix} \right.\] \[=\frac{\Gamma 2\Gamma 5/2}{\Gamma (2+5/2)}\] \[=\frac{1.3/2.1/2\Gamma 1/2}{\Gamma 9/2}\] \[(\because \Gamma 1/2=\sqrt{\pi })\] \[=\frac{3/4.\sqrt{\pi }}{7/2.5/2.3/2.1/2\sqrt{\pi }}=\frac{4}{35}\]
You need to login to perform this action.
You will be redirected in
3 sec
