Boole's Rule
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Calling Sequence
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ApproximateInt(f(x), x = a..b, method = boole, opts)
ApproximateInt(f(x), a..b, method = boole, opts)
ApproximateInt(Int(f(x), x = a..b), method = boole, 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 ApproximateInt(f(x), x = a..b, method = boole, opts) command approximates the integral of f(x) from a to b by using Boole's rule. 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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In the case that the widths of the subintervals are equal, the approximation can be written as
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Traditionally, Boole's rule is written as: given N, where N is a positive multiple of 3, and given equally spaced points , an approximation to the integral is
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By default, the interval is divided into equal-sized subintervals.
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This rule is also sometimes known as Bode's Rule, due to a misattribution in the literature. The command will accept either or method=bode.
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Examples
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See Also
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int, Newton-Cotes Rules, Simpson's 3/8 Rule, Simpson's Rule, Student, Student plot options, Student[Calculus1], Student[Calculus1][ApproximateInt], Student[Calculus1][ApproximateIntTutor], Student[Calculus1][RiemannSum], Student[Calculus1][VisualizationOverview], Trapezoidal Rule
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