Question

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?

Answer 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.