Question

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

Answer 1

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.