Region R is bounded by the curve

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

Problem

y=\sqrt{x}

, the

x

–axis, and the vertical line

x=9

. The region is revolved about the vertical line

x=-1

to generate a solid of revolution. (a) Rewrite the boundary curve in the form

x=f(y)

and state the lower and upper limits of

y

that describe Region R. (b) Using your expression from part (a), set up—but do not yet evaluate—an integral with respect to

y

that gives the exact volume of the solid. (c) Evaluate the integral from part (b) to obtain the exact volume.