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# gauss

Computes the definite integral of a function using the Gauss quadrature for 3 points.
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C++

## Gauss

 doublegauss( double (*f)(double)[function pointer] double a double b )[inline]
This module computes the area beneath a user supplied function using an approximation given by a certain weighted sum of function values.

Consider a function and two distinct abscissas . In order to compute an approximation of the definite integral: we will use the Gauss-Legendre quadrature formula for 3 points:

For fixed the error of this approximation is given by

### Example 1

In what follows an approximation is found for the definite integral and the absolute error from its actual value is estimated.
#include <codecogs/maths/calculus/quadrature/gauss.h>
#include <stdio.h>
#include <math.h>

// function to integrate
double f(double x)
{
return sin(x);
}

// the primitive of f, to estimate errors
double pf(double x)
{
return -cos(x);
}

int main()
{
// compute the approximate area
double fi = Maths::Calculus::Quadrature::gauss(f, 2, 3),

// use the Leibniz-Newton formula to find a more precise estimate
realfi = pf(3) - pf(2);

// display the result and error estimate
printf("      f(x) = sin(x)\n");
printf("   I(2, 3) = %.15lf\n", fi);
printf("real value = %.15lf\n", realfi);
printf("     error = %.15lf\n\n", fabs(fi - realfi));

return 0;
}

### Output

f(x) = sin(x)
I(2, 3) = 0.573845954654464
real value = 0.573845660053303
error = 0.000000294601161

### References

Mihai Postolache - "Metode Numerice", Editura Sirius

### Parameters

 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.

### Authors

Lucian Bentea (September 2006)
##### Source Code

Source code is available when you buy a Commercial licence.

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