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Lower Rectangle Method


New member
Aug 15, 2013
Can someone suggest a way to improve the lower rectangle method for area approximation...? I know one way is to increase the number of rectangles so if I put 100 instead of 5 rectangles i will get a better approximation. Another way it could be improved...?


Staff member
Feb 24, 2012
There is the midpoint rule, the trapezoidal rule, Simpson's rule, and higher order Newton-Cotes formulas. If you are in a calculus course, all of these will be introduced to you soon, except perhaps for the Newton-Cotes formulas.

Prove It

Well-known member
MHB Math Helper
Jan 26, 2012
As Mark has suggested, the best way to improve on the Left Hand Estimate is to not use it, but to use a more accurate method. Better yet perform the definite integral to get an exact answer. If worse comes to worse, do a Right Hand Estimate as well and average the results.


Well-known member
MHB Math Helper
Jan 29, 2012
In the case that a function is increasing (of decreasing) a "left hand" approximation is the same as your "lower rectangle" approximation and a "right hand" approximation is the same as an "upper rectangle" approximation. The average of the two, as Prove It suggests, is the same as the "trapezoid" method. I believe that "Simpson's rule" is the most accurate of the elementary methods for the same amount of work.