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-   -   Finds INTEGRAL of f(x) by Trapezoidal and Simpson method (http://www.go4expert.com/articles/integral-f-x-trapezoidal-simpson-method-t23016/)

 coderzone 14Aug2010 19:08

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); }```

 helloword 30Aug2010 21:54

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

oh very good

 helloword 30Aug2010 21:57

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

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

 shabbir 4Sep2010 12:21

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

Nominate this article for Article of the month - Aug 2010 before September 15 2010.

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