Question 1101661
If the area of the region bounded by the graph of y=x^3, the line x=2 and the x-axis is revolved about the line x=-1 then find the volume of the solid revolution. 
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The limits of x are 0 and 2.
Use shells:
Volume of a shell at x = dx*x^3*2pi*(x+1)
dV = 2pi*(x^4 + x^3)dx
Vol = 2pi*(x^5/5 + x^4/4)
0 --> 0
For x = 2:
Vol = 2pi*(32/5 + 4)
= 104pi/5 cubic units
=~ 65.345 cubic units