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

Write a program that will approximate the integral of

   f(x) = 2/sqrt(1-x^2)

The bounds of integration should be supplied by the
user, as well as the number of rectangles used in the
approximation.

Note:  The integral f(x) from 0 to 1 has a value
you should recognize!

Note:  You could change the function by changing a
single line in the code, in case you want to
approximate a different integral.
***************************************************/
#include "si204.h"
#include <math.h>

int main() {
  // Read a and b
  fputs("Enter integration bounds a and b: ", stdout);
  double a = readnum(stdin);
  double b = readnum(stdin);

  // Read n
  fputs("Enter n, the number of steps: ", stdout);
  int n = readnum(stdin);

  // Compute width of rectangles
  double w = (b - a) / n;

  // Initialize integral approximation value to zero
  double approx = 0.0;

  // update approximation from each step
  for(int i=0; i < n; i++) {
    // Compute evaluation point x
    double x = a + i*w;

    // Compute fucntion value at x
    // XXX: change this line to compute a different integral!
    double fx = 2.0 / sqrt(1.0 - x*x);

    // Add area of rectangle to approx
    approx += fx * w;
  }

  // Write out answer
  fputs("The integral is approximately ", stdout);
  writenum(approx, stdout);
  fputs("\n", stdout);

  return 0;
}