Riemann sum
(重定向自Upper sum)

![Riemann sum methods of x3 over [0,2] using 4 subdivisionsLeftRightMiddleTrapezoidalSimpson's Method](/uploads/202502/19/LeftRiemann2.svg2333.png)


In mathematics, a Riemann sum is an approximation that takes the form . It is named after German mathematician Bernhard Riemann. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations.