Volume of solid between y = x^(1/3) and x = 4y rotated about x-axis

[dan38]

Homework Statement

Question is:
FInd the volume for area bound between
y = x ^ (1/3)
x = 4y
About the x -axis

I found the volumes from 0 to 8 using the washer method and then multiplied that by 2 since they intersect at y = 0, -2 and 2 x = 0, 8 and -8
Is that wrong?
Cause my answer was double what it should have been..

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

Question is:
FInd the volume for area bound between
y = x ^ (1/3)
x = 4y
About the x -axis

I found the volumes from 0 to 8 using the washer method and then multiplied that by 2 since they intersect at y = 0, -2 and 2 x = 0, 8 and -8
Is that wrong?
Cause my answer was double what it should have been..

What does your integral look like?

 

[dan38]

In integrated the expression:

x^(2/3) - ( x^2/16)

 

[Mark44]

Is there something in the problem that you have overlooked? For example is the region that is rotated around the x-axis supposed to be only in the first quadrant? If so, then when you doubled your answer to account for the part of the region in the third quadrant, that would cause your answer to be too large by a factor of two.

Also, can you show the work you did in integrating?