How do you determine the volume of a solid created by revolving a function around an axis?

1 Answer
Jan 7, 2017

#"Volume" = pi int_a^b f(x)^2 dx#

Explanation:

Given a function #f(x)# and an interval #[a, b]# we can think of the solid formed by revolving the graph of #f(x)# around the #x# axis as a horizontal stack of an infinite number of infinitesimally thin disks, each of radius #f(x)#.

The area of a circle is #pir^2#, so the area of the circle at a point #x# will be #pi f(x)^2#.

The volume of the solid is then the infinite sum of the infinitesimally thin disks over the interval #[a, b]#

So:

#"Volume" = int_a^b pif(x)^2 dx = pi int_a^b f(x)^2 dx#