Consider the region bounded by the curves and in the first quadrant

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

Problem

Consider the region bounded by the curves

y=x^{2}

and

y=2x

in the first quadrant. When this region is revolved about the

y

-axis, what is the exact volume of the solid generated? (a)

\dfrac{16\pi}{3}

(b)

\dfrac{8\pi}{3}

(c)

\dfrac{4\pi}{3}

(d)

8\pi