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Lower Rectangle Method

rsyed5

New member
Aug 15, 2013
5
Hi,
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...?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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
1,403
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.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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.