Some functions that would be fun to integrate on (0, π].

y=[x*[1-x/pi]]^2

Analytic except at the endpoint, where it is C2. Integral can be done analytically.

y=1+cos([pi*cos(x)])

Analytic, infinite Fourier series, but the integral can't be done analytically.

y=sin(x)^4

Analytic, finite Fourier series, and the integral can be done analytically.

y=exp([-cos(2*x)])

Analytic, infinite Fourier series, but the integral cannot be done analytically

y=1/(2+cos(2*x))

Analytic, infinite Fourier series, integral can be done analytically.

Graph of the formula

This file was created by Graphing Calculator 3.5.
Visit Pacific Tech to download the helper application to view and edit these equations live.