The region bounded by the curves and for is revolved about the -axis

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

Problem

The region bounded by the curves

x = y^{2}

and

x = 4

for

0 \le y \le 2

is revolved about the

y

-axis. Which definite integral gives the volume of the resulting solid? (a)

V = 2\pi \displaystyle \int_{0}^{2} y\bigl(4 - y^{2}\bigr)\,dy

(b)

V = \pi \displaystyle \int_{0}^{2}\bigl(16 - y^{2}\bigr)\,dy

(c)

V = \pi \displaystyle \int_{0}^{2}\bigl(16 - y^{4}\bigr)\,dy

(d)

V = \pi \displaystyle \int_{0}^{2}\bigl(4 - y^{2}\bigr)^{2}\,dy