Chapter 6.3, Problem 25ES

(a) Use cylindrical shells to find the volume of the solid that is generated when the region under the curve

$y=x^3-3x^2+2x$

over $\left[0,1\right]$ is revolved about the $y\text{-axis}$ .

(b) For this problem, is the method of cylindrical shells easier or harder than the method of slicing discussed in the last section? Explain.