left hand rule

The left hand rule for computing the Riemann integral abf(x)𝑑x is


If the Riemann integral is considered as a measureMathworldPlanetmath of area under a curve, then the expressions f(a+(j-1)(b-an)) the of the rectangles, and b-an is the common of the rectangles.

The Riemann integral can be approximated by using a definite value for n rather than taking a limit. In this case, the partitionPlanetmathPlanetmath is {[a,a+b-an),,[a+(b-a)(n-1)n,b]}, and the function is evaluated at the left endpoints of each of these intervals. Note that this is a special case of a left Riemann sum in which the xj’s are evenly spaced.

Title left hand rule
Canonical name LeftHandRule
Date of creation 2013-03-22 15:57:38
Last modified on 2013-03-22 15:57:38
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 16
Author Wkbj79 (1863)
Entry type Theorem
Classification msc 41-01
Classification msc 28-00
Classification msc 26A42
Related topic RightHandRule
Related topic MidpointRule
Related topic RiemannSum
Related topic ExampleOfEstimatingARiemannIntegral