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Calculus (math)

The volume of the solid obtained by rotating the region enclosed by
y=1/x4,y=0,x=1,x=6
about the line x=−2 can be computed using the method of cylindrical shells via an integral.

it would be great if you can just even give me the function inside that I need to take the integral of?

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  1. You want to integrate along x, so the shells have thickness dx.

    The volume is thus

    v = ∫[1,6] 2πrh dx
    where r = x+2 and h = y = 1/x^4

    v = 2π∫[1,6] (x+2)/x^4 dx
    That's a nice easy integral to evaluate.

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