Simpson's 3-8th Rule - Maple Help
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Simpson's 3/8 Rule

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ApproximateInt(f(x), x = a..b, method = simpson[3/8], opts)

ApproximateInt(f(x), a..b, method = simpson[3/8], opts)

ApproximateInt(Int(f(x), x = a..b), method = simpson[3/8], 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 ApproximateInt(f(x), x = a..b, method = simpson[3/8], opts) command approximates the integral of f(x) from a to b by using Simpson's 3/8 rule.  This rule is also known as Newton's 3/8 rule. 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 , Simpson's 3/8 rule approximates the integral on each subinterval  by integrating the cubic function that interpolates the four points , , , and .  This value is

• 

In the case that the widths of the subintervals are equal, the approximation can be written as

  

Traditionally, Simpson's 3/8 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

• 

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

• 

For the options opts, see the ApproximateInt help page.

• 

This rule can be applied interactively, through the ApproximateInt Tutor.

Examples

(1)

(2)

To play the following animation in this help page, right-click (Control-click, on Mac) the plot to display the context menu.  Select Animation > Play.

See Also

Boole's Rules

Newton-Cotes Rules

plot/options

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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