Region lies in the first quadrant and is bounded by ,

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

Problem

Region

Q

lies in the first quadrant and is bounded by

y=\sqrt{x}

y=3

, and the

y

-axis. When

Q

is revolved about the

y

-axis, which pair of integrals both compute the volume of the resulting solid? (a)

V = 2\pi\displaystyle\int_{0}^{9} \bigl(3-\sqrt{x}\bigr)\,dx = \pi\displaystyle\int_{0}^{3} y^{2}\,dy

(b)

V = 2\pi\displaystyle\int_{0}^{9} x\bigl(3-\sqrt{x}\bigr)\,dx = \pi\displaystyle\int_{0}^{3} y^{4}\,dy

(c)

V = 2\pi\displaystyle\int_{0}^{3} y^{2}\bigl(3-y\bigr)\,dy = \pi\displaystyle\int_{0}^{9} \bigl(3-\sqrt{x}\bigr)^{2}\,dx

(d)

V = 2\pi\displaystyle\int_{0}^{3} y\bigl(3-y\bigr)\,dy = \pi\displaystyle\int_{0}^{9} x^{2}\,dx