What are the rules for setting up an integral of rotation?

Setting up an integral of rotation is used as a method of of calculating the volume of a 3D object formed by a rotated area of a 2D space. Finding the volume is similar to finding the area, but there is one additional component of rotating the area around a line of symmetry.

First the solid of revolution should be defined. The general function is y=f (x), on an interval [a, b].

Then the curve is rotated about a given axis to get the surface of the solid of revolution. That is the integral of the function.

It all depends of the function f (x), which must be known in order to calculate the integral.