(
Mathematics - Calculus)
For a positive function on the
real line, the integral of that
function over an interval describes the area between the function's
curve and the zero line.
There are several kinds of integration.
Most commonly known is the
Riemann integral. Other integrals include, but are not limited to, the
Darboux integral and the
Darboux-Stieltjes integral. Riemann integrals and Darboux integrals are very similar because if a function is Riemann
integrable, then it is Darboux integrable and vice versa, and the integrals have the same values. The
Darboux-Stieltjes integral is a generalization of the Riemann integral, and appears in the study of
probability.