A solid has base region bounded by the graph of and the -axis for

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

Problem

A solid has base region bounded by the graph of

y=\sqrt{x}

and the

x

-axis for

0\le x\le 9

. Cross sections perpendicular to the

x

-axis are squares. Which of the following definite integrals represents the volume

V

of the solid? (a)

\displaystyle \int_{0}^{3} y^{2}\,dy

(b)

\displaystyle \int_{0}^{9} \sqrt{x}\,dx

(c)

\displaystyle \int_{0}^{9} x\,dx

(d)

\displaystyle 2\int_{0}^{9} x\,dx