/*  Approximate the integral 

        integral of g(x) for x in [a,b]

    by subdividing the interval [a,b] into m subintervals of size
    delta, rescaling each subinterval to [-1,1] and applying the
    quadrature formula

        integral f(x) for x in [-1,1] = sum w[k] f(x[k])

    and then summing the results over all the subintervals.

    Note:  If you change the values of x[k] below, then you should
    also change the weights w[k] so that the equality

        integral x^j for x in [-1,1] = sum w[k] x[k]^j

    is exact for each j from 0 to K-1.  */

#include <stdio.h>
#include <math.h>

#define K 4
double x[K]={ -3.0/4, -1.0/4, 1.0/4, 3.0/4 };
double w[K]={ /* Please fill in these values */ };

double g(double x){
    return exp(-x*x);
}
double coats(double a,double delta){
    double s=0.0;
    for(int k=0;k<K;k++){
        s+=w[k]*g((x[k]+1)*delta/2+a);
    }
    return s*delta/2;
}
double ncquad(int m,double a,double b){
    double s=0.0,delta=(b-a)/m;
    for(int j=0;j<m;j++){
        s+=coats(a+j*delta,delta);
    }
    return s;
}

int main(){
    printf("This is problem 2 on quiz 2.\n");
    double y=ncquad(8,0,3);
    printf("Integral=%.14e\n",y);
    if(fabs(y-8.86207376544023e-01)<1e-11){
        printf("Congratulations!  Your answer is correct!\n");
    } else {
        printf("Please try again.  Your answer is incorrect.\n");
    }
    return 0;
}