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1. Multiple Application Trapezoidal Rule
2. Simple C Program For Trapezoidal Ruler
3. Trapezoidal Rule Calculator Wolfram

Controller: CodeCogs

Interface

Multiple Application Trapezoidal Rule

Overview

This module computes the area beneath either a user supplied function or a set of discrete points, using an approximation which assumes the function is linear between each two consecutive points.Consider a two times differentiable function , two distinct abscissas and a positive integer . Then the following approximation holds:with an error bound of:This is a quadrature formula known as the trapezoidal rule. From the formula of the error bound you may notice that e.g. if one doubles the number of points , the approximation error is decreased four times. To better understand how this rule works, observe the following picture - the area between abscissas and is approximated by a trapezoid.Below you will find examples that show how to use each version of the function and the error estimates in each case.

References:

• Mihai Postolache - 'Metode Numerice', Editura Sirius
• Mathworld, http://mathworld.wolfram.com/TrapezoidalRule.html

Authors

Lucian Bentea (September 2006)

Trapezoidal

doubletrapezoidal(	int	n
double	(*f)(double)[function pointer]
double	a
double	b	)

This version is to be used when you wish to pass the function to integrate as an argument, instead of passing an array with its values at distinct points.

Example 1

In what follows an approximation is found for the definite integraland the absolute error from its actual value is estimated.

Output

Parameters

n	the number of sample points of the function f, from which to approximate
f	the function to integrate
a	the inferior limit of integration
b	the superior limit of integration

Returns

The definite integral of the given function from a to b.

Source Code

Source code is available when you buy a Commercial licence.

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Trapezoidal

doubletrapezoidal(	int	n
const double*	values
double	a
double	b	)

This version is to be used when the function is not known analytically, but a table with its values at equally spaced abscissas is available.

Example 2

The code below gives an approximation for the definite integraland estimates the absolute error from its actual value.

Output

Parameters

n	the number of sample points of the function f, from which to approximate
values	an array with the values of the function at equally spaced abscissas
a	the inferior limit of integration
b	the superior limit of integration

Returns

The definite integral of the given function from a to b.

Source Code

Source code is available when you buy a Commercial licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.

Simple C Program For Trapezoidal Ruler

Trapezoidal Rule Calculator Wolfram