Midpoint Riemann Sum
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Calling Sequence
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RiemannSum(f(x), x = a..b, method = midpoint, opts)
RiemannSum(f(x), a..b, method = midpoint, opts)
RiemannSum(Int(f(x), x = a..b), method = midpoint, opts)
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Parameters
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f(x)
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algebraic expression in variable 'x'
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x
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name; specify the independent variable
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a, b
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algebraic expressions; specify the interval
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opts
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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
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Description
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The RiemannSum(f(x), x = a..b, method = midpoint, opts) command calculates the midpoint Riemann sum of f(x) from a to b. The first two arguments (function expression and range) can be replaced by a definite integral.
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If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.
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Given a partition of the interval , the midpoint Riemann sum is defined as:
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where the chosen point of each subinterval of the partition is the midpoint .
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By default, the interval is divided into equal-sized subintervals.
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For the options opts, see the RiemannSum help page.
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