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Left Riemann Sum
Calling Sequence
RiemannSum(f(x), x = a..b, method = left, opts)
RiemannSum(f(x), a..b, method = left, opts)
RiemannSum(Int(f(x), x = a..b), method = left, opts)
Parameters
f(x)
-
algebraic expression in variable 'x'
x
name; specify the independent variable
a, b
algebraic expressions; specify the interval
opts
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
Description
The RiemannSum(f(x), x = a..b, method = left, opts) command calculates the left 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 of the interval , the left Riemann sum is defined as:
where the chosen point of each subinterval of the partition is the left-hand point .
By default, the interval is divided into equal-sized subintervals.
For the options opts, see the RiemannSum help page.
This integration method can be applied interactively, through the ApproximateInt Tutor.
Examples
Other Riemann Sums
Lower Riemann Sum
Midpoint Riemann Sum
Right Riemann Sum
Upper Riemann Sum
See Also
plot/options, Student, Student plot options, Student[Calculus1], Student[Calculus1][ApproximateInt], Student[Calculus1][ApproximateIntTutor], Student[Calculus1][RiemannSum], Student[Calculus1][VisualizationOverview]
Download Help Document
