Use the Shell Method to Set Up and Evaluate the Integral

Multiple Choice

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. $y = 14 x - x ^ { 2 } , x = 0 , y = 49$

A) $V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 49 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 6 } \pi$
B) $V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 98 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 6 } \pi$
C) $V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 196 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 6 } \pi$
D) $V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 196 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 3 } \pi$
E) $V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 49 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 3 } \pi$