Arogya Thapa Magar

C program for Simpson's 1/3 Rule | C Programming

Arogya Thapa Magar at February 11, 2019 0

C program for Simpson's 1/3 Rule

Before Starting the program let us know about the Simpson's 1/3 rule and How it works?

Simpson’s 1/3 Rule The trapezoidal rule was based on approximating the integrand by a first-order polynomial and then integrating the polynomial over an interval of integration. Simpson’s 1/3 rule is an extension of the Trapezoidal rule where the integrand is approximated by a second-order polynomial.

Simple Simpsons one third Formula

Composite Simpsons one third formula

Application :

It is used when it is very difficult to solve the given integral mathematically.

This rule gives approximation easily without actually knowing the integration rules

C program to for Composite Simpsons 1/3 rule

#include<stdio.h>
#include<conio.h>
#include<math.h>
//#define f(x) sqrt(1-((x)*(x)))
//#define f(x) exp(-1*(x*x))
//#define f(x) (cos(x)*cos(x))
//#define f(x) sin(x)
#define f(x) exp(-1*(x/2))
int main(){
 
 float a,h,x0,xn,fx0,fxn,term,v;
 int i,k;
 printf("Composite Simpson's 1/3 rule'");
 printf("\nEnter Lower and Upper Limit \n");
 scanf("%f%f",&x0,&xn);
 printf("\nEnter number of segments (should be multiple of 2)\n");
 scanf("%d",&k);
 h=(xn-x0)/k;
 fx0=f(x0);
 fxn=f(xn);
 term=f(x0)+f(xn);
 
 for(i=1;i<=(k-1);i=i+2){
  a=x0+i*h;
  term=term+4*(f(a));
 }
 
 for(i=2; i<=(k-2);i=i+2){
  a=x0+i*h;
  term=term+2*(f(a));
 }
 
 v=h/3*term;
 
 printf("\nValue of Integration= %f\n",v);
 return 0;
}

C program for Simpsons 1/3 rule

#include<stdio.h>
#include<conio.h>
#include<math.h>
//#define f(x) 3*(x)*(x)+2*(x)-5
//#define f(x) sin(x)
//#define f(x) exp(-1*(x/2))
#define f(x) 3*x*x
int main(){
 
 float h,x0,x1,x2,fx0,fx1,fx2,v;
 int n=2;
 printf("Simpson's 1/3 rule'");
 printf("\nEnter Lower and Upper Limit \n");
 scanf("%f%f",&x0,&x2);
 h=(x2-x0)/n;
 x1=x0+h;
 fx0=f(x0);
 fx1=f(x1);
 fx2=f(x2);
 v=h/3*(fx0+4*fx1+fx2);
 printf("\nValue of Integration= %f\n",v);
 return 0;
}

C Program to calculate value using composite trapezoidal rule | C Programming

Arogya Thapa Magar at February 05, 2019 0

C programming to calculate value using composite trapezoidal rule

#include<stdio.h>
#include<conio.h>
#include<math.h>
#define F(x) 2*x
int main()
{
int n,i;
float a,b,h,x,sum=0,integral;
printf("Enter the two limits:\n");
scanf("%f%f",&a,&b);
printf("Enter the difference n:\n");
scanf("%d",&n);
h=(b-a)/n;
for(i=1;i<n;i++)
{
x=a+i*h;
sum=sum+F(x);
}
integral=(h/2)*(F(a)+F(b)+2*sum);
printf("\nThe integral is: %f\n",integral);
return 0;

}

C Programming Codes To Compute Value Using Trapezoidal Rule

Arogya Thapa Magar at February 05, 2019 0

C Programming Codes To Compute Value Using Trapezoidal Rule

#include<stdio.h>
#include<conio.h>
#include<math.h>
#define F(x) exp(-(x/2))
int main()
{
int a,b,h;
float i,x,y;
printf("Enter the value for lower and upper limit\n");
scanf("%d%d",&a,&b);
h=b-a;//Calculating height
x=F(a);//Calculation Function and storing in x and y.
y=F(b);
i=h*((x+y)/2);
printf("The Intregrated Value is %.3f",i);
}