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Integral with one variable

int Integrate(
INTERVAL_VECTOR (* TheIntervalFunction)
(int,int,INTERVAL_VECTOR &),
INTERVAL & TheDomain,
int Iteration,
double Accuracy,
INTERVAL & Result)
The simplest integration procedure of ALIAS that should be used only for the simplest function.
• TheIntervalFunction: a procedure in MakeF format to interval evaluate the function
• TheDomain: integration domain
• Iteration: this procedure uses a set of boxes and Iteration is the maximum number of boxes that can be used
• Accuracy: desired accuracy for the integration: the width of the result should be lower than this number
• Result: the range for the integral
This procedure returns 1 if the calculation has been successful, -1 if the desired accuracy cannot be reached and -2 if the number of boxes has been exceeded.

If the function is at least twice differentiable it is possible to use:

int IntegrateTrapeze(
INTERVAL_VECTOR (* TheIntervalFunction)
(int,int,INTERVAL_VECTOR &),
INTERVAL_VECTOR (* SecondDerivative)
(int,int,INTERVAL_VECTOR &),
INTERVAL & TheDomain,
int Iteration,
double Accuracy,
INTERVAL & Result)

int IntegrateRectangle(
INTERVAL_VECTOR (* TheIntervalFunction)
(int,int,INTERVAL_VECTOR &),
INTERVAL_VECTOR (* SecondDerivative)
(int,int,INTERVAL_VECTOR &),
INTERVAL & TheDomain,
int Iteration,
double Accuracy,
INTERVAL & Result)
The procedure SecondDerivative in MakeF format allows to interval evaluate the second derivative of the function.

Alternatively it is possible to use:

int IntegrateTaylor(
INTERVAL_VECTOR (* CoeffTaylor)
(int,int,INTERVAL_VECTOR &),
int Order,
INTERVAL & TheDomain,
int Iteration,
double Accuracy,
INTERVAL & Result)
The procedure CoeffTaylor, in MakeF format, should provide the interval evaluation of the Taylor coefficients of the function up to the order Order+1 (i.e. Order+2) coefficients).    Next: Integral with multiple variable Up: Definite integrals Previous: Definite integrals   Contents
Jean-Pierre Merlet 2012-12-20