calculus cylindrical shells?
The volume of the solid obtained by rotating the region enclosed by
y = 1/x^4, y = 0, x = 1, x = 4
about the line x = -4 can be computed using the method of cylindrical shells via an integral; what is the integral? What is the volume?
Comments
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v=2pi int fromx=1 to 4 of (x+4)/x^4dx
v=2pi[-x^(-2)/2 -4x^(-3)/3]
=(3 and 9/16 )pi
integral from [1,4]( (-4 - 1/x^4)^2 dx )