I am trying to complete the task of integrating with the right rectangle rule, but I am stuck at one moment. The first two values are being outputted, but further ones are just 0... The task is about starting with iteration count 3 and continuing up to 512, by multiplying iteration count by 2 every time. I feel something is wrong here, but I can't see what. Let the test values be, as in the task: lower: -3, upper: 6, starting iteration count: 3

#include <iostream>

using namespace std;

double Function(double x)
{
    if (x < 0)
        return (1 / sqrt(25   (3 * x)));
    else
        return pow(x, 2)   0.2;
}

double Integrate(int upper, int lower, int iteration_count)
{
    double pre_sum = (double)((double)(upper - lower) / iteration_count);
    double sum = 0;
    for (int i = 1, step ; i < iteration_count; i  )
    {
        sum  = Function(lower   pre_sum   i);
    }

    return sum * pre_sum;
}

int main()
{
    int upper, lower, iteration_count;
    cout << "Enter lower bound: ";
    cin >> lower;
    cout << "Enter upper bound: ";
    cin >> upper;
    cout << "Enter iteration count: ";
    cin >> iteration_count;

    for (int i = iteration_count; i < iteration_count * 512; i=i*2)
    {
        cout << "Integration result: " << Integrate(upper, lower, i) << endl;
    }
    return 0;
}

But values keep increasing drastically:

Enter lower bound: -3
Enter upper bound: 6
Enter iteration count: 3
Integration result: 16.2
Integration result: 33.0094
Integration result: 198.962
Integration result: 1138.16
Integration result: 5578.55
Integration result: 24809.2
Integration result: 104733
Integration result: 430463
Integration result: 1.74547e 06

CodePudding user response：

1. Change sum = Function(lower pre_sum i); to sum = Function(lower pre_sum * i);. That is, you should multiply by i rather than add it. i represents the index of the iteration (indexed by 1 for right-rectangle integration; indexed by 0 for left-rectangle integration.)
2. Change for (int i = 1, step ; i < iteration_count; i ) to for (int i = 1; i <= iteration_count; i ). That is, check for less-than-or-equal rather than less-than inequality. Otherwise, the number of iterations performed is actually one less than iteration_count, which is likely unintended behavior. step was also removed, since it's dead code.

Output:

Enter lower bound: -3
Enter upper bound: 6
Enter iteration count: 3
Integration result: 136.8
Integration result: 103.081
Integration result: 87.911
Integration result: 80.7481
Integration result: 77.2722
Integration result: 75.5606
Integration result: 74.7114
Integration result: 74.2885
Integration result: 74.0774