To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is
A) the Disk Method.
B) the Shell Method.
C) the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.

Question

To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is 
A) the Disk Method. 
B) the Shell Method. 
C) the Disk and Shell Methods. 
D) Integration by Parts. 
E) none of these methods.

Quizplus · Accepted Answer

The Shell Method is the most convenient method to compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis. This is because the region is defined by vertical lines, and the shells (cylindrical shells) are aligned along the y-axis. Thus, integrating with respect to y using the Shell Method is easier than integrating with respect to x using the Disk Method. The Disk and Shell Methods could also work, but the Shell Method is more efficient in this specific case. Integration by Parts is not applicable for finding volumes. Therefore, the answer is B) the Shell Method.

To Compute the Volume of the Solid Obtained by Rotating