To find the volume generated when the region bounded by and is revolved about the -axis

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

To find the volume generated when the region bounded by

x=y^{2}

and

x=4y

is revolved about the

y

-axis, a student must decide whether to integrate with respect to

x

y

. Which of the following most strongly supports integrating with respect to

y

? (a) Because integrating with respect to

y

means using washers instead of shells, and washers are always simpler. (b) Because the equations are already written as

x

in terms of

y

, so integrating with respect to

y

is the only possible choice. (c) Integrating with respect to

x

would require subtracting two inverse functions for every slice, whereas integrating with respect to

y

allows the radii to be read directly from

x=y^{2}

and

x=4y

. (d) Because integrating with respect to

y

makes every washer’s inner radius

0

, eliminating the need to subtract two areas.