In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet.
One of those is
This integral is not absolutely convergent, and so the integral is not even defined in the sense of Lebesgue integration, but it is defined in the sense of the Riemann integral or the Henstock–Kurzweil integral. The value of the integral (in the Riemann or Henstock sense) can be derived in various ways. For example, the value can be determined from attempts to evaluate a double improper integral, or by using differentiation under the integral sign.
Famous quotes containing the word integral:
“Make the most of your regrets; never smother your sorrow, but tend and cherish it till it come to have a separate and integral interest. To regret deeply is to live afresh.”
—Henry David Thoreau (1817–1862)