SOLUTION: Find the volumes of the solids generated by revolving the regions bounded by the lines and curves : y=x^3 (x cube) y=0 x=2

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Question 556723: Find the volumes of the solids generated by revolving the regions bounded by the lines and curves :
y=x^3 (x cube)
y=0
x=2

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
First, draw the graph of the function and the rotation. You didn't specify which axis you rotate the region about. I'll assume you rotate about the x-axis.

We want to evaluate the integral



This is equal to

evaluated at x = 2, minus the value at x = 0, or simply

.