Changes

==Riemann integral==

==Riemann integral==

The [[Riemann Integral|Riemann integral]] is the common definition today of the integral, as first put on a rigorous mathematical foundation by Riemann.  The Riemann integral is, in essence, the definite integral:

The [[Riemann Integral|Riemann integral]] is the common definition today of the integral in introductions to analysis, as first put on a rigorous mathematical foundation by Riemann.  The Riemann integral is, in essence, the definite integral:

:<math>\int_a^b f(x)\,dx</math>

:<math>\int_a^b f(x)\,dx</math>

It is defined as the sum of infinitesimal segments of the area under the function on a graph, between ''f(a)'' and ''f(b)''.

It is defined as the sum of infinitesimal segments of the x-axis of the area under the function on a graph, between ''f(a)'' and ''f(b)''.

 

As it is more versatile, the [[Lebesgue]] Integral has superseded this definition.

==Additional concepts named after Riemann==

==Additional concepts named after Riemann==