Homework Help: calculus

Posted by Michelle on Saturday, January 24, 2009 at 5:53pm.

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?

calculus - Damon, Saturday, January 24, 2009 at 6:08pm
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)
so
dV = dx *2pi *(4-x) (x^2-3x)
integrate from x = 0 to x = 3

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