Riemann Sum
المؤلف:
New York: Wiley, pp. 324-327, 1999.Calculus: A New Horizon, 6th ed.Anton, H.
المصدر:
New York: Wiley, pp. 324-327, 1999.Calculus: A New Horizon, 6th ed.Anton, H.
الجزء والصفحة:
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25-8-2018
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Riemann Sum
Let a closed interval ![[a,b]](http://mathworld.wolfram.com/images/equations/RiemannSum/Inline1.gif)
be partitioned by points 
, where the lengths of the resulting intervals between the points are denoted 
, 
, ..., 
. Let 
be an arbitrary point in the 
th subinterval. Then the quantity
is called a Riemann sum for a given function 
and partition, and the value 
is called the mesh size of the partition.
If the limit of the Riemann sums exists as 
, this limit is known as the Riemann integral of 
over the interval ![[a,b]](http://mathworld.wolfram.com/images/equations/RiemannSum/Inline12.gif)
. The shaded areas in the above plots show the lower and upper sums for a constant mesh size.
REFERENCES:
New York: Wiley, pp. 324-327, 1999.Calculus: A New Horizon, 6th ed.Anton, H.
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