Posted by Michelle on .
A question on my math homework that I can't seem to solve...
Rotate the region bounded by y=x^2-3x and the x-axis about the line x=4. Set up the integral to find the volume of the solid.
I'm pretty sure that the integral is in terms of (dy), and has bounds of 0-4. Using the slice method, the radius is (4-x), but I need the radius in terms of y. I tried solving for x to use substitution, but it didn't work.
What would this equation be, solved for x, and what would the integral be for finding the volume?
lets do it as thin walled cylinders rather than as circular slices.
each cylinder is at height y and at radius (4 - x) with wall thickness dx
The cylinders start at x = 0 and end at x = 3 (where y = 0, we are looking at a sliced bagel with a donut hole)
the circumference of each cylinder is 2 pi r = 2 pi (4-x)
dV = dx *2pi *(4-x) (x^2-3x)
integrate from x = 0 to x = 3