left hand rule
The left hand rule for computing the Riemann integral b∫af(x)𝑑x is
b∫af(x)𝑑x=limn→∞n∑j=1f(a+(j-1)(b-an))(b-an). |
If the Riemann integral is considered as a measure 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 partition 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 |