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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