Let S be the solid obtained when the region bounded by the parabola and the…

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let S be the solid obtained when the region bounded by the parabola

y=x^{2}

and the horizontal line

y=4

is revolved about the

y

-axis. (a) Express each boundary curve in the form

x

as a function of

y

and determine the

y

-interval over which the region exists. (b) Write a definite integral that represents the volume of S in terms of

y

. Clearly identify the outer and inner radii. (c) Evaluate the integral to obtain the exact volume of S.