Consider the region enclosed by the graphs of and for

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the region enclosed by the graphs of

y=x^{2}

and

y=2x

for

x\ge 0

. Cross sections of a solid are taken perpendicular to the

y

-axis. Each cross section is a rectangle whose height is exactly twice the length of its base. (a) Express the length of the base

b(y)

of a typical rectangle in terms of

y

. (b) Write, but do not evaluate, a definite integral in terms of

y

that gives the volume of the solid.