The Region Under the Curve $y = 3 \sin ^ { 2 } x , 0 \leq x \leq \pi$

question 101

Multiple Choice

The region under the curve $y = 3 \sin ^ { 2 } x , 0 \leq x \leq \pi$ is rotated about the $x$ -axis. Find the volume of the resulting solid. Select the correct answer.

• A) \(\frac { 9 } { \pi ^ { 2 } }\)
• B) \(\frac { 27 } { 8 } \pi ^ { 2 }\)
• C) \(\frac { 3 } { \pi }\)
• D) \(\frac { \pi ^ { 2 } } { 9 }\)
• E) \(\frac { \pi } { 9 }\)

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