/***************************************************
Integration of f(x) by simple end-point approximation

Write a program that will approximate the integral of 

   f(x) = (x*sin(x) - 1)*log(x),

where "log" is the natural logarithm. The bounds of
integration should be supplied by the user, as well
as the number of rectangles used in the approximation.
We'll discuss the simple approximation scheme we'll
use in class.

Note:  The integral of f(x) from 2.5 to 3.5 is
approximately -0.8147741401.

Note:  Both log() and sin() are functions in cmath.
***************************************************/
#include <iostream>
#include <string>
#include <cmath>
using namespace std;

int main()
{
  // Read a and b
  double a, b;
  char c;
  cout << "Enter integrations bounds (a,b): ";
  cin >> c >> a >> c >> b >> c;

  int n;
  cout << "Enter n: ";
  cin >> n;

  double w = (b-a) / n;

  double total = 0;
  for (int i=0; i<n; i++) {

	double x = a + w * i; // get effective x

	double fx = (x*sin(x) - 1)*log(x);

	cout << x << " " << fx;
	// add in area from that block
	total = total + w * fx;

  }

  cout << "total is: " << total << endl;

  return 0;

}