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Upper Riemann Sum

Calling Sequence

RiemannSum(f(x), x = a..b, method = upper, opts)

RiemannSum(f(x), a..b, method = upper, opts)

RiemannSum(Int(f(x), x = a..b), method = upper, opts)




algebraic expression in variable 'x'



name; specify the independent variable

a, b


algebraic expressions; specify the interval



equation(s) of the form option=value where option is one of boxoptions, functionoptions, iterations, method, outline, output, partition, pointoptions, refinement, showarea, showfunction, showpoints, subpartition, view, or Student plot options; specify output options



The RiemannSum(f(x), x = a..b, method = upper, opts) command calculates the upper Riemann sum of f(x) from a to b. The first two arguments (function expression and range) can be replaced by a definite integral.


If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.


Given a partition P=a=x0,x1,...,xN=b of the interval a,b, the upper Riemann sum is defined as:

i=1Nfxi* xixi1


where the chosen point of each subinterval xi1,xi of the partition is a point xi*  such that fxfxi* for all x in xi1,xi.


By default, the interval is divided into 10 equal-sized subintervals.


For the options opts, see the RiemannSum help page.


This integration method can be applied interactively, through the ApproximateInt Tutor.









Other Riemann Sums


Left Riemann Sum


Lower Riemann Sum


Midpoint Riemann Sum


Right Riemann Sum

See Also

plot/options, Student, Student plot options, Student[Calculus1], Student[Calculus1][ApproximateInt], Student[Calculus1][ApproximateIntTutor], Student[Calculus1][RiemannSum], Student[Calculus1][VisualizationOverview]

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