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^23x and the xaxis 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 04. Using the slice method, the radius is (4x), 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 (4x)
so
dV = dx *2pi *(4x) (x^23x)
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=9yy^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