Homework Help: Trouble finding volume of curve shell method

1. Feb 19, 2013

togo

1. The problem statement, all variables and given/known data
Given the following curve:
y = x^3
Use shell method and rotate around x-axis to determine the volume
bounded region: y = 8, x = 0

2. Relevant equations
2pixy

3. The attempt at a solution
x(x^3) = x^4
Integrate
x^4 = 1/5 x^5
1/5(8)^5 = 6553.6
*2 = 13107.2 pi

the answer should be 768/7 pi, where did I go wrong? thanks.

Last edited: Feb 19, 2013
2. Feb 19, 2013

Staff: Mentor

What is the complete problem statement? You need to have some finite region in the plane to start with.

3. Feb 19, 2013

togo

bounded region: y = 8, x = 0

4. Feb 19, 2013

eumyang

For starters, if you are supposed to use shell method, revolving around the x-axis, than the integrand needs to be in terms of y, not x.

5. Feb 19, 2013

haruspex

As eumyang notes, you've used the disc method, not the shell method, but it still should produce the right answer. Your answer is wrong because you've calculated the wrong region. It is not bounded by y=0, it's bounded by y=8. Draw the bounded region in the XY plane.