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

## Answer This Question

## Related Questions

- Calculus - This problem set is ridiculously hard. I know how to find the volume ...
- Calculus - Let R be the region bounded by the curve x=9y-y^2 and the y- axis. ...
- please help calculus - find the volume of the solid formed by revolving the ...
- Math - Calculus - The region in the first quadrant bounded by y=6x^2 , 2x+y=8, ...
- Calculus check - The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-...
- Calculus - I'm having trouble with the following problem: Find the volume of the...
- calculus - Find the volume of the solid generated by revolving the region about ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...

More Related Questions