Question

public double Integral(double[] x, double intPointOne, double intPointTwo)
{
    double integral = 0;
    double i = intPointOne;
    do
    {
        integral += Function(x[i])*.001;
        i = i + .001;
    }
    while (i <= intPointTwo);
    return integral;
}

Here’s a function I have to integrate a function from x1-x2 simply using a summation of parts. How can I make this loop more efficient (using less loops), but more accurate?

Where Function changes every iteration, but it should be irrelevant as it’s order of magnitude (or boundary) should stay relatively the same…

Answer 1

1) look into section 4.3 of http://apps.nrbook.com/c/index.html for a different algorithm.

2) To control the accuracy/speed factor you may need to specify the bounds x_low and x_high as well as how many slices you want in the integral. So your function would look like this

// Integrate function f(x) using the trapezoidal rule between x=x_low..x_high
double Integrate(Func<double,double> f, double x_low, double x_high, int N_steps)
{
    double h = (x_high-x_low)/N_steps;
    double res = (f(x_low)+f(x_high))/2;
    for(int i=1; i < N; i++)
    {
        res += f(x_low+i*h);
    }
    return h*res;
}

Once you understand this basic integration, you can move on to more elaborate schemes mentioned in Numerical Recipies and other sources.

To use this code issue a command like A = Integrate( Math.Sin, 0, Math.PI, 1440 );