Here is the region we need to rotate:
The graph of the area bounded by `y=x^3`, `x=0` and `y=4`.
And here is the volume generated when we rotate the region around the `y`-axis:
The volume generated when revolving the curve bounded by `y=x^3`, `x=0` and `y=4` around the `y`-axis.
We first must express x in terms of y, so that we can apply the volume of solid of revolution formula.
If y = x3 then x = y1/3
The formula requires x2, and on squaring we have x2 = y2/3
`text[Vol] = pi int_c^d x^2 dy`
`=pi int_0^4 y^[2//3] dy`