Volume of a solid of revolution

When the graph of a function $f(x)$ is rotated about the x-axis, it forms a solid of revolution. Its volume is the sum of infinitely thin disks of radius $f(x)$:

$V=\pi\int_a^b [f(x)]^2\,dx$

The calculator takes $f$ as a polynomial, squares it, integrates and evaluates on the interval $[a,b]$.

Classic results: rotating $f(x)=x$ from $0$ to $h$ gives a cone ($V=\tfrac13\pi h^3$), and $f(x)=r$ (a constant) gives a cylinder ($V=\pi r^2 h$). It is a bridge between integral calculus and solid geometry.