The region bounded above by and below by the –axis for is the base of a solid

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

Problem

The region bounded above by

y=x^{2}

and below by the

x

–axis for

0\le x\le 2

is the base of a solid. Cross sections taken perpendicular to the

x

–axis are squares. Which of the following integrals represents the volume

V

of the solid? (a)

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

(b)

\displaystyle 2\int_{0}^{2} x^{4}\,dx

(c)

\displaystyle \int_{0}^{2} x^{4}\,dx

(d)

\displaystyle \int_{0}^{4} x^{4}\,dx