Let be the region bounded by the –axis and the parabola

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

Problem

Let

R

be the region bounded by the

x

–axis and the parabola

y=4x-x^{2}

. When

R

is revolved about the

x

–axis, what is the volume of the solid that is generated? (a)

\displaystyle \frac{256\pi}{15}

(b)

\displaystyle \frac{640\pi}{15}

(c)

\displaystyle \frac{512\pi}{15}

(d)

\displaystyle \frac{1024\pi}{15}