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

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

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
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

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