• # question_answer The area enclosed by the curve$y={{x}^{5}}$, the $x-$axis and the ordinates $x=-1,\,\,x=1$ is A) $0$                                     B) $\frac{1}{3}$C) $\frac{1}{6}$                                   D)  None

Required area                 $=\int\limits_{-1}^{1}{|y|dx}=\int\limits_{-1}^{1}{|{{x}^{5}}|}\,dx=2\int\limits_{0}^{1}{|{{x}^{5}}|dx}$                 $=2\int\limits_{0}^{1}{{{x}^{5}}dx}=2\left[ \frac{{{x}^{6}}}{6} \right]_{0}^{1}=\frac{2}{6}=\frac{1}{3}$