d3r5.cpp

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#include "iostream.h"
#include "math.h"

double func2(double x)
{
    return 1.0 / sqrt(x);
}

double fint2(double x)
{
    //integral of func2
    return 2.0 * sqrt(x);
}

void midpnt(double a, double b, double& s, int& n)
{
	double del,ddel,sum,x;
	int it,tnm,j;
    if (n == 1)
	{
        s = (b - a) * func2(0.5 * (a + b));
        it = 1;
	}
    else
	{
        it = (int)pow(3, n - 2);
        tnm = it;
        del = (b - a) / (3.0 * tnm);
        ddel = del + del;
        x = a + 0.5 * del;
        sum = 0.0;
        for (j = 1; j<=it; j++)
		{
            sum = sum + func2(x);
            x = x + ddel;
            sum = sum + func2(x);
            x = x + del;
        }
        s = (s + (b - a) * sum / tnm) / 3.0;
    }
}

void main()
{
    //program d3r5
    //driver for routine midpnt
    const int nmax = 10;
    double s,a = 0.0;
    double b = 1.0;
    cout<<endl;
    cout<<"integral of func2 computed with midpnt"<<endl;
	cout.precision(6);
    cout<<endl;
    cout<<"actual value of integral is"<<"  ";
    cout<<(fint2(b) - fint2(a))<<endl;
    cout<<endl;
    cout<<"    n    approx.integral"<<endl;
	cout.setf(ios::fixed|ios::right);
	for (int i = 1; i<=nmax; i++)
	{
        midpnt(a, b, s, i);
		cout.width(5);
        cout<<i;
		cout.width(15);
        cout<<s<<endl;
    }
}