To compute the volume of the solid obtained by rotating the region between the line and the curve in the first quadrant about the y-axis, the most convenient method is
A) the Shell Method.
B) the Disk Method.
C) the Shell Method in addition to the Disk Method.
D) Integration by Parts.
E) none of these methods.

Question

To compute the volume of the solid obtained by rotating the region between the line  and the curve  in the first quadrant about the y-axis, the most convenient method is 
A) the Shell Method. 
B) the Disk Method. 
C) the Shell Method in addition to the Disk Method. 
D) Integration by Parts. 
E) none of these methods.

Quizplus · Accepted Answer

The Shell Method is the most convenient method for finding the volume of the solid generated by rotating the region between the line and the curve about the y-axis in the first quadrant. This is because the shape of the region is better suited for the cylindrical shells used in the Shell Method, rather than the discs used in the Disk Method. Integration by Parts is not a relevant method for finding the volume of this solid.

To Compute the Volume of the Solid Obtained by Rotating