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).