Use the method of cylindrical shells to find the volume generated
by rotating the region bounded by the given curves about the
specified axis. Sketch the region and a typical shell.
y = 4x - x^2, y = 3; about x = 1
The Attempt at a Solution
int(2*pi*(1-x)*(3-4*x+x^2), x = 0 .. 1) = 11pi/6
This is the only problem on the book that I can't really understand. The correct answer is 8pi/3 according on the odd answers on the back page.
Increasing the upper limit to 2 gives the correct answer. But why? Isn't it I'll just integrate until 1 so I can get a y = 3. Why 2?