Finds INTEGRAL of f(x) by Trapezoidal and Simpson method

Finds INTEGRAL of f(x) by Trapezoidal and Simpson method Simultaneously

Code:

  TRAPEZOIDAL RULE :-
  Integral of F(x) in between the limits a and b is given by
  =(h/2)*(y[0]+2(y[1]+y[2]+y[3]+..y[n-1])+y[n])
  where y[i]=F(x[i]),
  x[i]=x[i-1]+h,
  h=(b-a)/n.

Code:

  SIMPSON RULE :-
  Integral of F(x) in between the limits a and b is given by
  =(h/3)*(y[0]+4(y[1]+y[3]+y[5]+..y[n-1])+2*(y[2]+y[4]+y[6]+..y[n-2])+y[n])
  where y[i],x[i],h as defined above but n needed to be even

The CODE

Code:

#include <stdio.h>
#include <conio.h>
#define N 20
#define n 10
#define F(x) (1/(1+x))
float trap(float,float);
float simp(float,float);
void main()
{
	float a,b,t,s;
	printf("\nEnter the values of a and b\n");
	scanf("%f%f",&a,&b);
	t=trap(a,b);
	s=simp(a,b);
	printf("\nTrapezoidal answer = %g\n",t);
	printf("\nSimpson answer = %g\n",s);
	printf("\nPress any key to exit\n");
	getch();
}
float trap(float a,float b)
{
	float h,x[N],y[N],ans;
	int i;
	h=(b-a)/n;
	y[0]=F(a);
	ans=y[0];
	x[0]=a;
	for(i=1;i<n;i++)
	{
		x[i]=x[i-1]+h;
		y[i]=F(x[i]);
		ans=ans+2*y[i];
	}
	y[n]=F(b);
	ans=ans+y[n];
	ans=ans*h/2;
	return(ans);
}
float simp(float a,float b)
{
	float h,x[N],y[N],ans;
	int i;
	h=(b-a)/n;
	y[0]=F(a);
	ans=y[0];
	x[0]=a;
	for(i=1;i<n;i+=2)
	{
		x[i]=x[i-1]+h;
		y[i]=F(x[i]);
		ans=ans+4*y[i];
	}
	for(i=2;i<n;i+=2)
	{
		x[i]=x[i-1]+h;
		y[i]=F(x[i]);
		ans=ans+2*y[i];
	}
	y[n]=F(b);
	ans=ans+y[n];
	ans=ans*h/3;
	return(ans);
}

 

oh very good

 

hello ,i'm study c++ now, i‘m from china ,my english is not so good ，I hope everyone can learn together