Use the Shell Method to Set Up and Evaluate an Integral

Multiple Choice

Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. $$y = 25 - x ^ { 2 } , y = 0$$

A) $V = 4 \pi \int _ { 0 } ^ { 5 } x \left( 25 - x ^ { 2 } \right) d x = 625 \pi$
B) $V = 4 \pi \int _ { - 5 } ^ { 5 } x \left( 25 - x ^ { 2 } \right) d x = 625 \pi$
C) $V = 2 \pi \int _ { - 5 } ^ { 0 } x \left( 25 - x ^ { 2 } \right) d x = 625 \pi$
D) $V = 2 \pi \int _ { 0 } ^ { 5 } x \left( 25 - x ^ { 2 } \right) d x = \frac { 625 } { 2 } \pi$
E) $V = 2 \pi \int _ { - 5 } ^ { 5 } x \left( 25 - x ^ { 2 } \right) d x = \frac { 625 } { 2 } \pi$