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单词 LeftHandRule
释义

left hand rule


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

abf(x)𝑑x=limnj=1nf(a+(j-1)(b-an))(b-an).

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.

Titleleft hand rule
Canonical nameLeftHandRule
Date of creation2013-03-22 15:57:38
Last modified on2013-03-22 15:57:38
OwnerWkbj79 (1863)
Last modified byWkbj79 (1863)
Numerical id16
AuthorWkbj79 (1863)
Entry typeTheorem
Classificationmsc 41-01
Classificationmsc 28-00
Classificationmsc 26A42
Related topicRightHandRule
Related topicMidpointRule
Related topicRiemannSum
Related topicExampleOfEstimatingARiemannIntegral
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更新时间:2025/5/4 9:28:54