A) \[\frac{-2}{3}\]
B) \[\frac{-4}{5}\]
C) \[\frac{2}{3}\]
D) \[\frac{-5}{6}\]
Correct Answer: B
Solution :
\[{{I}_{n}}=\int\limits_{0}^{1}{{{(x\,\ln \,x)}^{n}}dx}\] \[{{I}_{n}}=\left. \left( {{\left( \ln x \right)}^{n}}.\frac{{{x}^{n+1}}}{n+1} \right) \right|_{0}^{1}-\frac{n}{n+1}\int\limits_{0}^{1}{{{x}^{n}}{{(\ln x)}^{n-1}}dx}\] \[\therefore \]\[{{I}_{4}}=\frac{-4}{5}\int\limits_{0}^{1}{{{x}^{4}}\ln {{x}^{3}}dx}\]You need to login to perform this action.
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