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Lower Riemann Sum
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Calling Sequence
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RiemannSum(f(x), x = a..b, method = lower, opts)
RiemannSum(f(x), a..b, method = lower, opts)
RiemannSum(Int(f(x), x = a..b), method = lower, 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 = lower, opts) command calculates the lower 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 ![P = (a = x[0], x[1], () .. (), x[N] = b)](/support/helpjp/helpview.aspx?si=4873/file04928/math145.png) of the interval  , the lower Riemann sum is defined as:
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![sum(f(x[i]^`* `)*(x[i]-x[i-1]), i = 1 .. N)](/support/helpjp/helpview.aspx?si=4873/file04928/math153.png)
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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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