Is my integration algorithm correct? Also can we improve this on parallel processing and efficiency? The code is in C#

Question

How do i better calculate the definite integral? I am using a function to integrate and another to find the factorial recursively.

I'l like to better the algorithm or the efficiency or even the accuracy for that matter.

    public static double testStatistic(double meanTreatmentSumOfSquares, double meanErrorSumOfSquares)
    {
        return (meanTreatmentSumOfSquares / meanErrorSumOfSquares);
    }

    public static double pValue(double fStatistic, int degreeNum, int degreeDenom)
    {
        double pValue = 0;
        pValue = integrate(0, fStatistic, degreeNum, degreeDenom);

        return pValue;

    }

    public static double integrate(double start, double end, int degreeFreedomT, int degreeFreedomE)
    {
        int iterations = 100000;
        double x, dist, sum = 0, sumT = 0;
        dist = (end - start) / iterations;
        for (int i = 1; i <= iterations; i++)
        {
            x = start + i * dist;
            sumT += integralFunction(x - dist / 2, degreeFreedomT, degreeFreedomE);
            if (i < iterations)
            {
                sum += integralFunction(x, degreeFreedomT, degreeFreedomE);
            }
        }
        sum = (dist / 6) * (integralFunction(start, degreeFreedomT, degreeFreedomE) + integralFunction(end, degreeFreedomT, degreeFreedomE) + 2 * sum + 4 * sumT);
        return sum;
    }

    public static double integralFunction(double x, int degreeFreedomT, int degreeFreedomE)
    {
        double temp=0;
        temp = ((Math.Pow(degreeFreedomE, degreeFreedomE / 2) * Math.Pow(degreeFreedomT, degreeFreedomT / 2)) / (factorial(degreeFreedomE / 2 - 1) * factorial(degreeFreedomT / 2 - 1))) * (factorial(((degreeFreedomT + degreeFreedomE) / 2 - 1)))*((Math.Pow(x, degreeFreedomE / 2 - 1)) / (Math.Pow((degreeFreedomT + degreeFreedomE * x), ((degreeFreedomE + degreeFreedomT) / 2))));
        return temp;
    }

    public static double factorial(double n)
    {
        if (n == 0)
        {
            return 1.0;
        }
        else
        {
            return n * factorial(n - 1);
        }
    }
}
}

Answer 1

change the for loop as below to remove the if condition inside the for loop:

for (int i = 1; i < iterations; i++)
{
    x = start + i * dist;
    sumT += integralFunction(x - dist / 2, degreeFreedomT, degreeFreedomE);
    sum += integralFunction(x, degreeFreedomT, degreeFreedomE);
}
x = start + iterations * dist;
sumT += integralFunction(x - dist / 2, degreeFreedomT, degreeFreedomE);

EDIT: Also you might want to use this compiler option -finline-functions(works in gcc and icc. check for equivalent in C#). The call to the function integralFunction (a simple 1 line function) will be inlined during compilation and function call overhead for each iteration can be removed