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# Program to estimate the Integral value of the function at the given points from the given data using Simpson's 1/3 Rule

Posted By: Easy Tutor     Category: C++ Programming     Views: 4272

## Code for Program to estimate the Integral value of the function at the given points from the given data using Simpson's 1/3 Rule in C++ Programming

```/*************************************************************************//*************************************************************************       A C++ Program to estimate the Integral value of the function at       the given points from the given data using Simpson's 1/3 Rule.  *************************************************************************//*************************************************************************/

# include <iostream.h>
# include   <stdlib.h>
# include   <string.h>
# include    <stdio.h>
# include    <conio.h>
# include     <math.h>

constint max_size=13;

int n=0;
int top=-1;
int choice=0;

longdouble h=0;
longdouble a=0;
longdouble b=0;
longdouble estimated_value=0;

longdouble xn[max_size]={0};
longdouble fx[max_size]={0};

char Fx[100]={NULL};
char Stack[30][30]={NULL};
char Postfix_expression[30][30]={NULL};

/*************************************************************************//*************************************************************************///------------------------  Funcion Prototypes  -------------------------///*************************************************************************//*************************************************************************/void push(constchar *);
void convert_ie_to_pe(constchar *);

constchar* pop( );
constlongdouble evaluate_postfix_expression(constlongdouble);

void show_screen( );
void clear_screen( );
void get_input( );
void apply_simpsons_rule( );
void show_result( );

/*************************************************************************//*************************************************************************///------------------------------  main( )  ------------------------------///*************************************************************************//*************************************************************************/int main( )
{
clrscr( );
textmode(C4350);

show_screen( );
get_input( );
apply_simpsons_rule( );
show_result( );

getch( );
return 0;
}

/*************************************************************************//*************************************************************************///------------------------  Funcion Definitions  ------------------------///*************************************************************************//*************************************************************************//*************************************************************************///--------------------------  show_screen( )  ---------------------------///*************************************************************************/void show_screen( )
{
cprintf("\n********************************************************************************");
cprintf("***************************-                         -**************************");
cprintf("*--------------------------- ");

textbackground(1);
cprintf(" Numerical Integration ");
textbackground(8);

cprintf(" --------------------------*");
cprintf("*-*************************-                         -************************-*");
cprintf("*-****************************************************************************-*");

for(int count=0;count<42;count++)
cprintf("*-*                                                                          *-*");

gotoxy(1,46);
cprintf("*-****************************************************************************-*");
cprintf("*------------------------------------------------------------------------------*");
cprintf("********************************************************************************");

gotoxy(1,2);
}

/*************************************************************************///-------------------------  clear_screen( )  ---------------------------///*************************************************************************/void clear_screen( )
{
for(int count=0;count<37;count++)
{
gotoxy(5,8+count);
cout<<"                                                                        ";
}

gotoxy(1,2);
}

/*************************************************************************///--------------------------  push(const char*)  ------------------------///*************************************************************************/void push(constchar* Operand)
{
if(top==(max_size-1))
{
cout<<"Error : Stack is full."<<endl;
cout<<"\n        Press any key to exit.";

getch( );
exit(0);
}

else
{
top++;
strcpy(Stack[top],Operand);
}
}

/*************************************************************************///------------------------------  pop( )  -------------------------------///*************************************************************************/constchar* pop( )
{
char Operand[40]={NULL};

if(top==-1)
{
cout<<"Error : Stack is empty."<<endl;
cout<<"\n        Press any key to exit.";

getch( );
exit(0);
}

else
{
strcpy(Operand,Stack[top]);
strset(Stack[top],NULL);
top--;
}

return Operand;
}

/*************************************************************************///--------------------  convert_ie_to_pe(const char*)  ------------------///*************************************************************************/void convert_ie_to_pe(constchar* Expression)
{
char Infix_expression[100]={NULL};
char Symbol_scanned[30]={NULL};

push("(");
strcpy(Infix_expression,Expression);
strcat(Infix_expression,"+0)");

int flag=0;
int count_1=0;
int count_2=0;
int equation_length=strlen(Infix_expression);

if(Infix_expression[0]=='(')
flag=1;

do
{
strset(Symbol_scanned,NULL);

if(flag==0)
{
int count_3=0;

do
{
Symbol_scanned[count_3]=Infix_expression[count_1];

count_1++;
count_3++;
}
while(count_1<=equation_length &&
Infix_expression[count_1]!='(' &&
Infix_expression[count_1]!='+' &&
Infix_expression[count_1]!='-' &&
Infix_expression[count_1]!='*' &&
Infix_expression[count_1]!='/' &&
Infix_expression[count_1]!='^' &&
Infix_expression[count_1]!=')');

flag=1;
}

elseif(flag==1)
{
Symbol_scanned[0]=Infix_expression[count_1];

count_1++;

if(Infix_expression[count_1]!='(' &&
Infix_expression[count_1]!='^' &&
Infix_expression[count_1]!='*' &&
Infix_expression[count_1]!='/' &&
Infix_expression[count_1]!='+' &&
Infix_expression[count_1]!='-' &&
Infix_expression[count_1]!=')')
flag=0;

if(Infix_expression[count_1-1]=='(' &&
(Infix_expression[count_1]=='-' ||
Infix_expression[count_1]=='+'))
flag=0;
}

if(strcmp(Symbol_scanned,"(")==0)
push("(");

elseif(strcmp(Symbol_scanned,")")==0)
{
while(strcmp(Stack[top],"(")!=0)
{
strcpy(Postfix_expression[count_2],pop( ));

count_2++;
}

pop( );
}

elseif(strcmp(Symbol_scanned,"^")==0 ||
strcmp(Symbol_scanned,"+")==0 ||
strcmp(Symbol_scanned,"-")==0 ||
strcmp(Symbol_scanned,"*")==0 ||
strcmp(Symbol_scanned,"/")==0)
{
if(strcmp(Symbol_scanned,"^")==0)
{  }

elseif(strcmp(Symbol_scanned,"*")==0 ||
strcmp(Symbol_scanned,"/")==0)
{
while(strcmp(Stack[top],"^")==0 ||
strcmp(Stack[top],"*")==0 ||
strcmp(Stack[top],"/")==0)
{
strcpy(Postfix_expression[count_2],pop( ));

count_2++;
}
}

elseif(strcmp(Symbol_scanned,"+")==0 ||
strcmp(Symbol_scanned,"-")==0)
{
while(strcmp(Stack[top],"(")!=0)
{
strcpy(Postfix_expression[count_2],pop( ));

count_2++;
}
}

push(Symbol_scanned);
}

else
{
strcat(Postfix_expression[count_2],Symbol_scanned);

count_2++;
}
}
while(strcmp(Stack[top],NULL)!=0);

strcat(Postfix_expression[count_2],"=");
count_2++;
}

/*************************************************************************///----------  evaluate_postfix_expression(const long double)  -----------///*************************************************************************/constlongdouble evaluate_postfix_expression(constlongdouble x)
{
longdouble function_value=0;

int count_1=-1;

char Symbol_scanned[30]={NULL};

do
{
count_1++;

strcpy(Symbol_scanned,Postfix_expression[count_1]);

if(strcmp(Symbol_scanned,"^")==0 ||
strcmp(Symbol_scanned,"*")==0 ||
strcmp(Symbol_scanned,"/")==0 ||
strcmp(Symbol_scanned,"+")==0 ||
strcmp(Symbol_scanned,"-")==0)

{
char Result[30]={NULL};
char Operand[2][30]={NULL};

strcpy(Operand[0],pop( ));
strcpy(Operand[1],pop( ));

longdouble operand[2]={0};
longdouble result=0;

char *endptr;

for(int count_2=0;count_2<2;count_2++)
{
int flag=0;

if(Operand[count_2][0]=='-')
{
int length=strlen(Operand[count_2]);

for(int count_3=0;count_3<(length-1);count_3++)
Operand[count_2][count_3]=Operand[count_2][(count_3+1)];

Operand[count_2][count_3]=NULL;

flag=1;
}

if(strcmp(Operand[count_2],"x")==0)
operand[count_2]=x;

elseif(strcmp(Operand[count_2],"e")==0)
operand[count_2]=2.718282;

elseif(strcmp(Operand[count_2],"sinx")==0)
operand[count_2]=sinl(x);

elseif(strcmp(Operand[count_2],"cosx")==0)
operand[count_2]=cosl(x);

elseif(strcmp(Operand[count_2],"tanx")==0)
operand[count_2]=tanl(x);

elseif(strcmp(Operand[count_2],"lnx")==0)
operand[count_2]=logl(x);

elseif(strcmp(Operand[count_2],"logx")==0)
operand[count_2]=log10l(x);

else
operand[count_2]=strtod(Operand[count_2],&endptr);

if(flag)
operand[count_2]*=-1;
}

switch(Symbol_scanned[0])
{
case'^' : result=powl(operand[1],operand[0]);
break;

case'*' : result=operand[1]*operand[0];
break;

case'/' : result=operand[1]/operand[0];
break;

case'+' : result=operand[1]+operand[0];
break;

case'-' : result=operand[1]-operand[0];
break;
}

gcvt(result,25,Result);

push(Result);
}

elseif(strcmp(Symbol_scanned,"=")!=0)
push(Symbol_scanned);
}
while(strcmp(Symbol_scanned,"=")!=0);

char Function_value[30]={NULL};
char *endptr;

strcpy(Function_value,pop( ));
function_value=strtod(Function_value,&endptr);

return function_value;
}

/*************************************************************************///-----------------------------  get_input( )  --------------------------///*************************************************************************/void get_input( )
{
do
{
clear_screen( );

gotoxy(6,9);
cout<<"Number of Sub-Intervals :";

gotoxy(6,10);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(20,13);
cout<<"[ min. n = 2  |  max. n = 12 ]";

gotoxy(6,12);
cout<<"Enter the max. number of sub-intervals = n = ";

cin>>n;

if(n<2 || n>12)
{
gotoxy(12,25);
cout<<"Error : Wrong Input. Press <Esc> to exit or any other key";

gotoxy(12,26);
cout<<"        to try again.";

n=int(getche( ));

if(n==27)
exit(0);
}
}
while(n<2 || n>12);

gotoxy(6,16);
cout<<"Enter the value of Lower limit = a = ";

cin>>a;

gotoxy(6,18);
cout<<"Enter the value of Upper Limit = b = ";

cin>>b;

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

gotoxy(6,24);
cout<<"Input Mode :";

gotoxy(6,25);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(8,28);
cout<<"Press : ";

gotoxy(10,30);
cout<<"- 'Y' or <Enter> to enter function";

gotoxy(10,32);
cout<<"- 'N' or <Any other key> to enter values of the function";

gotoxy(8,35);

char Choice=NULL;

Choice=getch( );

if(Choice=='y' || Choice=='Y' || int(Choice)==13)
{
choice=1;

gotoxy(28,35);
cout<<"Y";
}

else
{
gotoxy(28,35);
cout<<"N";
}

gotoxy(25,43);
cout<<"Press any key to continue...";

getch( );

if(choice)
{
clear_screen( );

gotoxy(6,10);
cout<<"Non-Linear Function :";

gotoxy(6,11);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(6,37);
cout<<"Note : Write the function with proper Braces ( ) e.g; 2x+3 as (2*x)+3";

gotoxy(6,40);
cout<<"Available Operators  :  ^ (raised to power) , * , / , + , -";

gotoxy(6,42);
cout<<"Available Operands   :  x , e , sinx , cosx , tanx , lnx , logx ,";

gotoxy(6,44);
cout<<"                        n = any number";

gotoxy(6,14);
cout<<"Enter the Function : f(x) = ";

cin>>Fx;

convert_ie_to_pe(Fx);
}

clear_screen( );

gotoxy(6,9);
cout<<"Data Points & Values of Function :";

gotoxy(6,10);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(25,12);
cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

gotoxy(25,13);
cout<<"³       x       ³     f(x)      ³";

gotoxy(25,14);
cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

gotoxy(25,15);
cout<<"³               ³               ³";

for(int count_1=0;count_1<=n;count_1++)
{
gotoxy(25,(wherey( )+1));
cout<<"³               ³               ³";

gotoxy(25,(wherey( )+1));
cout<<"³               ³               ³";
}

gotoxy(25,(wherey( )+1));
cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";

xn[0]=a;

for(int count_2=0;count_2<n;count_2++)
xn[(count_2+1)]=(xn[count_2]+h);

gotoxy(25,16);

for(int count_3=0;count_3<=n;count_3++)
{
gotoxy(27,wherey( ));
cout<<xn[count_3];

if(choice)
{
fx[count_3]=evaluate_postfix_expression(xn[count_3]);

gotoxy(43,wherey( ));
cout<<fx[count_3];
}

else
{
gotoxy(43,wherey( ));
cin>>fx[count_3];
}

if(choice)
gotoxy(25,(wherey( )+2));

else
gotoxy(25,(wherey( )+1));
}

gotoxy(25,43);
cout<<"Press any key to continue...";

getch( );
}

/*************************************************************************///----------------------  apply_simpsons_rule( )  -----------------------///*************************************************************************/void apply_simpsons_rule( )
{
longdouble temp=0;

estimated_value=(fx[0]+fx[n]);
estimated_value*=h;
estimated_value/=3;

temp=0;

for(int count_1=2;count_1<=(n-2);count_1+=2)
temp+=fx[count_1];

temp*=(2*h);
temp/=3;

estimated_value+=temp;

temp=0;

for(int count_2=1;count_2<=(n-1);count_2+=2)
temp+=fx[count_2];

temp*=(4*h);
temp/=3;

estimated_value+=temp;
}

/*************************************************************************///-----------------------------  show_result( )  ------------------------///*************************************************************************/void show_result( )
{
clear_screen( );

gotoxy(6,9);
cout<<"Simpson's 1/3 Rule :";

gotoxy(6,10);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(8,12);
cout<<" bô";

gotoxy(10,13);
cout<<"³f(x)dx ÷ (h/3)(f0+fn) + (2h/3)[f2+f4+...+f(n-2)] +";

gotoxy(50,15);
cout<<"(4h/3)[f1+f3+...+f(n-1)]";

gotoxy(8,14);
cout<<" aõ";

gotoxy(6,17);
cout<<"              bô";

gotoxy(6,19);
cout<<"              aõ";

gotoxy(6,18);
cout<<"Estimation of  ³f(x)dx :";

gotoxy(6,20);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(8,23);
cout<<"Estimated Integral Value = ";

cout<<estimated_value;

gotoxy(1,2);
}
```
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