- #1
flyingpig
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Homework Statement
Use the method of cylindrical shells to nd the volume of the solid obtained by rotating
the region bounded by the curves y = x4, y = 1, x = 0 about the y-axis. Sketch the region and a typical shell
The Attempt at a Solution
I am just going to set it up, but I am not going to evaluate it
[tex]V = 2\pi \int_{0}^{1} x (x^4) dx[/tex]
My friend thinks it should be
[tex]V = 2\pi \int_{-1}^{1} x (x^4) dx[/tex]
Mine yields [tex]\frac{\pi}{3}[/tex] and my friend yields [tex]\frac{2\pi}{3}[/tex]
My argument is that we are only rotating the first quadrant. If we take the negative quadrant, it's meaningless. I am not even sure what we get if we take the negative quadrant, does it make it thicker?
EDIT: It is y = x4, not x2
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