Find the Volume of the Solid Generated by Revolving the Region

question 7

Multiple Choice

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the $x$ -axis and the curve $y = x \cos x , 0 \leq x \leq \pi / 2$ about the $y$ -axis.

• A) \(\frac { \pi ^ { 3 } } { 2 } - 4 \pi\)
• B) \(\frac { \pi ^ { 3 } } { 2 } + 2 \pi ^ { 2 } - 4 \pi\)
• C) \(\frac { \pi ^ { 2 } } { 2 } - 4 \pi\)
• D) \(\frac { \pi ^ { 3 } } { 2 } - 8 \pi\)

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