question_answer

The volume of the solid formed by rotating, the area enclosed between the curve \[y={{x}^{2}}\] and the line \[y=1\] about \[y=1\] is (in cubic unit):

A) \[9\pi /5\]                          

B) \[2\pi /5\]

C) \[8\pi /3\]                          

D) \[7\pi /5\]

Correct Answer: B

Solution :

\[\therefore \]Required volume\[=\int_{-1}^{1}{\pi {{y}^{2}}dx}\]                 \[=\pi \int_{-1}^{1}{{{x}^{4}}dx}=2\pi \left[ \frac{{{x}^{5}}}{5} \right]_{0}^{1}\]