Mathematics

Problem

The region in the first quadrant bounded by the curve

y = 3x - x^{2}

and the

x

-axis is revolved about the

x

-axis. Which of the following definite integrals represents the volume

V

of the solid generated? a)

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

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

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

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