To calculate the value of an integer using Trapezoidal rule both when functional values are both given and values NOT given independently

Engg - Numerical Methods

Trapezoidal rule can be applied to find the value of a limiting integer programmatically in both cases whether individual functional values are given or not. A complete algorithm follows the both process below.

/*********

Trapezoidal rule complete algorithm

1. start

2. read n= no of intervals

3. read initial and final values ie a,b

4. h=(b-a)/n;

5. set x[0]=a; x[n]=b;



6. next element

i= 1 to n-1

x[i]=x[i-1]+h



7. evaluating/reading function

i=0 to n

f[i]=function or input functional values as cin<



8. 1st &last terms

sum=f[0]+f[n]



9. i= 1 to n-1

sum= sum + 2 * ( f[i] )



10. sum=h/2*sum



11. display sum



12. stop

***********/





//To calculate the value of an integer using Trapeziodal Rule (no corressponding functional values provided)



#include

#include

#include

#include



void main()

{

double n,i,a,b;

double x[20],f[20], sum;

float h;

clrscr();



cout<<<"Enter no of intervals: ";

cin>>n;



cout<<<"Enter limiting values:\t";

cin>>a>>b;



h=(b-a)/n;

x[0]=a;

x[n]=b;



for(i=1;i<=n-1;i++)

{

x[i]=(x[i-1]+h);

}



for(i=0;i<=n;i++)

{

f[i]=exp(x[i]*tan(x[i]));

}



sum=f[0]+f[n];



for(i=1;i<=n-1;i++)

{

sum=sum+(2*f[i]);

}



sum=(h/2.0)*sum;



cout<<<"The required integral value = "<



getch();

}

/* To evaluate value of an integral using Trapezoidal Rule when the functional values are given */



#include

#include

#include

#include

void main()

{

double n,a,b,h,sum,x[20],i,f[20];



clrscr();

cout<<"To Calculate The Integral Value Using Trapezoidal Rule"<

cout<

cout<<"The given functional vaue is e^(x*tanx) \n"<

cout<<"Enter the Number of interval ";

cin>>n;

cout<<"There are "<<<" intervals\n"<

cout<<"Enter the initial point\t"<

cin>>a;

cout<<"Enter the final point\t"<

cin>>b;

cout<<"The limit of integration is from "<<<"to"<<<

h=(b-a)/n;

x[0]=a;

x[n]=b;

cout<

for(i=1;i<=n-1;i++)

{

x[i]=x[i-1]+h;

}



cout<<"Enter the functional value accordingly \n";

for(i=0;i<=n;i++)

{

cout<<"f"<<<"= ";

// f[i]=exp(x[i]*tan(x[i])) ;

cin>>f[i];

}



sum=f[0]+f[n];

for(i=1;i<=n-1;i++)

{

sum=sum+2*f[i];

}

sum=(h/2)*sum;



cout<<"The required value of integration is"<

getch();

}





To calculate the value of an integer using Trapezoidal rule both when functional values are given and values NOT given in C++ Programming Language for Numerical Methods for Engineering Students