#include<stdio.h>
#include<stdlib.h>
#include<math.h>
double INV_SQRT_2PI= 0.39894228;						/*1/sqrt(2*pi)*/
double a, b, u, U, O, c, left, right, d, approx, x;
double epsilon= 0.0000001;								/*epsilon defined as 0.0000001*/
double f(double x);										/*prototype functions*/
double S(double a, double b);
double asimpson(double a, double b, double approx, double epsilon);
 
 
int main(void)
{	
	printf("Enter x Value: ");
	scanf("%lf", &x);
	printf("Enter Mean: ");
	scanf("%lf", &U);
	printf("Enter Standard Deviation: ");
	scanf("%lf", &O);
	double pdf, u;
	u=((x-U)/O);
	pdf=((1/2)+INV_SQRT_2PI * asimpson(0,u,S(0,u),epsilon));
 
	printf("pdf= %f",pdf);
 
return 0;
}
double f(double x)
{	
	return (exp(double(x*x*(-1))/2));
}
double S(double a,double b)
{	
	return ((b-a)/6)*(f(a)+(4*f((a+b)/2))+f(b));
}
double asimpson(double a,double b,double approx, double epsilon)
{
	approx= S(a,b);
	c=((a+b)/2);
	left=S(a,c);
	right=S(c,b);
	d=((left+right-approx)/15);
	if(abs(d)<=epsilon)
		return (left+right+d);
	return (asimpson(a,c,left,epsilon/2)+asimpson(c,b,right,epsilon/2));
}