The shell has the radius x, the cricumference is `2pi*x` and the height is `x^3` , hence, the volume can be evaluated, using the method of cylindrical shells, such that:
`V = 2pi*int_1^2 x*(x^3) dx`
`V = 2pi*int_1^2 x^4dx`
Using the formula `int x^n dx = (x^(n+1))/(n+1) ` yields:
`V = 2pi*x^5/5|_1^2`
`V = 2pi*(2^5 - 1^5)/5`
`V = (62*pi)/5`
Hence, evaluating the volume, using the method of cylindrical shells, yields `V = (62*pi)/5.`
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