Trouble finding volume of curve shell method

[togo]

Homework Statement

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

Homework Equations

2pixy

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.

 

[Mark44]

Homework Statement

Given the following curve:
y = x^3
Use shell method and rotate around x-axis to determine the volume

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

Homework Equations

2pixy

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.

 

[togo]

bounded region: y = 8, x = 0

 

[eumyang]

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

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.

 

[haruspex]

where did I go wrong? .

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.