Calculate the Riemann sum of 1 + e^x for 0 < x < 1.

makefile

TARGET = riemann

all: $(TARGET)

$(TARGET): $(TARGET).cpp
	g++ -Wall -Wextra -O2 $(TARGET).cpp -o $(TARGET)

Riemann.cpp

#include <iostream>
#include <cmath>

using namespace std;

double f(double x)
{
    return 1 + exp(x);
}

double s(double h = 0.000009)
{
    double s = 0;
    for(double x = 0; x < 1; x += h)
        s += f(x);

    return s * h;
}

double epsilon(double h = 0.000009)
{
    return abs(s(h) - exp(1));
}

double small_h()
{
    for(double h = 0.1; h > 0; h /= 2)
        if(epsilon(h) <= 1e-5)
            return 2 * h;

    return -1;
}

int main()
{
    double h = small_h();

    cout.precision(7);
    cout << "s = " << s(h) << endl;
    cout << "ε = " << epsilon(h) << endl;
    cout << "h = " << h << endl;

    return 0;
}