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