Part I Write a program that takes in the following two 10-element arrays. The fi
ID: 3694622 • Letter: P
Question
Part I
Write a program that takes in the following two 10-element arrays. The first array is x an independent variable, the second array is y which is a function of x (y = f(x)).
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
y = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36}
With h = 1
Use the composite trapezoidal rule to compute the integral of f(x) from x = 0 to x = 9;
Use the composite Simpson Rule and compute the integral of f(x) from x = 0 to x = 9.
Display the results on the screen.
Part II:
For the previous program (the integrals one):
Create a Structure type called DataForFinal
This structure will have the following fields:
1) 10 element double array
2) 10 element double array
3) double variable
4) double variable
Create a structure and name it with your name
In the fields of this structure save the arrays x, and y and the variables containing the integrals using the trapezoidal and simpson rule methods.
Print the integral results on the screen using the fields in the array.
Explanation / Answer
Solution:Please follow these programs using simpson methods and trapeziodal methods
Implement Simpson method:
#include<stdio.h>
#include<conio.h>
#include<math.h>
char postfix[10];
float stack[10];
char stack1[10];
int top=-1,top1=-1;
float eval(char postfix[], float x1);
void infix_postfix(char infix[]);
main()
{
float x0, xn, h, s,e1,e2, e3;
char exp[80];
int i,l=0;
int arr[n] = {0,1,2,3,4,5,6,7,8,9}
clrscr();
printf(" Enter an expression: ");
gets(exp);
puts("Enter x0, xn and number of sub-intervals: ");
scanf("%f%f%d", &x0, &xn, &n);
h=(xn-x0)/n;
if(exp[0]=='l'&& exp[1]=='o'&& exp[2]=='g')
{
l=strlen(exp);
for(i=0;i<l-3; i++)
arr[0]=exp[i+3];
arr[i]='';
infix_postfix(arr);
e1=eval(postfix,x0);
e2=eval(postfix,xn);
e3=4*eval(postfix, x0+h);
s=log(e1)+log(e2)+log(e3);
for (i=3;i<=n-1;i+=2)
s+=4*eval(postfix,x0+i*h)+2*eval(postfix, x0+(i-1)*h);
}
else
{
infix_postfix(exp);
s=eval(postfix,x0)+eval(postfix,xn)+4*eval(postfix, x0+h);
for (i=3;i<=n-1;i+=2)
s+=4*eval(postfix,x0+i*h)+2*eval(postfix, x0+(i-1)*h);
}
printf("The value of integral is %6.3f ",(h/3)*s);
return(0);
}
/*Inserting the operands in a stack. */
void push(float item)
{
if(top==99)
{
printf(" The stack is full");
getch();
exit(0);
}
else
{
top++;
stack[top]=item;
}
return;
}
/*Removing the operands from a stack. */
float pop()
{
float item;
if(top==-1)
{
printf(" The stack is empty ");
getch();
}
item=stack[top];
top--;
return (item);
}
void push1(char item)
{
if(top1==9)
{
printf(" The stack is full");
getch();
exit(0);
}
else
{
top1++;
stack1[top1]=item;
}
return;
}
/*Removing the operands from a stack. */
char pop1()
{
char item;
if(top1==-1)
{
printf(" The stack1 is empty ");
getch();
}
item=stack1[top1];
top1--;
return (item);
}
/*Converting an infix expression to a postfix expression. */
void infix_postfix(char infix[])
{
int i=0,j=0,k;
char ch;
char token;
for(i=0;i<9;i++)
postfix[i]=' ';
push1('?');
i=0;
token=infix[i];
while(token!='')
{
if(isalnum(token))
{
postfix[j]=token;
j++;
}
else if(token=='(')
{
push1('(');
}
else if(token==')')
{
while(stack1[top1]!='(')
{
ch=pop1();
postfix[j]=ch;
j++;
}
ch=pop1();
}
else
{
while(ISPriority(stack1[top1])>=ICP(token))
{
ch=pop1();
postfix[j]=ch;
j++;
}
push1(token);
}
i++;
token=infix[i];
}
while(top1!=0)
{
ch=pop1();
postfix[j]=ch;
j++;
}
postfix[j]='';
}
/*Determining the priority of elements that are placed inside the stack. */
int ISPriority(char token)
{
switch(token)
{
case '(':return (0);
case ')':return (1);
case '+':return (2);
case '-':return (3);
case '*':return (4);
case '/':return (5);
case '?':return (6);
default: printf("Invalid expression");
}
return 0;
}
/*Determining the priority of elements that are approaching towards the stack. */
int ICP(char token)
{
switch(token)
{
case '(':return (10);
case ')':return (9);
case '+':return (7);
case '-':return (7);
case '*':return (8);
case '/':return (8);
case '':return (0);
default: printf("Invalid expression");
}
return 0;
}
/*Calculating the result of expression, which is converted in postfix notation. */
float eval(char p[], float x1)
{
float t1,t2,k,r;
int i=0,l;
l=strlen(p);
while(i<l)
{
if(p[i]=='x')
push(x1);
else
if(isdigit(p[i]))
{
k=p[i]-'0';
push(k);
}
else
{
t1=pop();
t2=pop();
switch(p[i])
{
case '+':k=t2+t1;
break;
case '-':k=t2-t1;
break;
case '*':k=t2*t1;
break;
case '/':k=t2/t1;
break;
default: printf(" Invalid expression");
}
push(k);
}
i++;
}
if(top>0)
{
printf("You have entered the operands more than the operators");
exit(0);
}
else
{
r=pop();
return (r);
}
return 0;
}
2)Implement Trapezoidal method:
#include<stdio.h>
#include<conio.h>
#include<math.h>
char postfix[10];
float stack[10];
char stack1[10];
int top=-1,top1=-1;
float eval(char postfix[], float x1);
void infix_postfix(char infix[]);
main()
{
float x0, xn, h, s,e1,e2;
char exp[80];
int i,l=0;
int arr[n] = {0,1,2,3,4,5,6,7,8,9}
clrscr();
printf(" Enter an expression: ");
gets(exp);
puts("Enter x0, xn and number of subintervals");
scanf("%f%f%d", &x0, &xn, &n);
h=(xn-x0)/n;
if(exp[0]=='l'&& exp[1]=='o'&& exp[2]=='g')
{
l=strlen(exp);
for(i=0;i<l-3; i++)
arr[0]=exp[i+3];
arr[i]='';
infix_postfix(arr);
e1=eval(postfix,x0);
e2=eval(postfix,xn);
s=log(e1)+log(e2);
for (i=1;i<=n-1;i++)
s+=2*log(eval(postfix,x0+i*h));
}
else
{
infix_postfix(exp);
s=eval(postfix,x0)+eval(postfix,xn);
for (i=1;i<=n-1;i++)
s+=2*eval(postfix,x0+i*h);
}
printf("Value of the integral is %6.3f ",(h/2)*s);
return(0);
}
/*Inserting the operands in a stack. */
void push(float item)
{
if(top==99)
{
printf(" The stack is full");
getch();
exit(0);
}
else
{
top++;
stack[top]=item;
}
return;
}
/*Removing the operands from a stack. */
float pop()
{
float item;
if(top==-1)
{
printf(" The stack is empty ");
getch();
}
item=stack[top];
top--;
return (item);
}
void push1(char item)
{
if(top1==9)
{
printf(" The stack is full");
getch();
exit(0);
}
else
{
top1++;
stack1[top1]=item;
}
return;
}
/*Removing the operands from a stack. */
char pop1()
{
char item;
if(top1==-1)
{
printf(" The stack1 is empty ");
getch();
}
item=stack1[top1];
top1--;
return (item);
}
/*Converting an infix expression to a postfix expression. */
void infix_postfix(char infix[])
{
int i=0,j=0,k;
char ch;
char token;
for(i=0;i<79;i++)
postfix[i]=' ';
push1('?');
i=0;
token=infix[i];
while(token!='')
{
if(isalnum(token))
{
postfix[j]=token;
j++;
}
else if(token=='(')
{
push1('(');
}
else if(token==')')
{
while(stack1[top1]!='(')
{
ch=pop1();
postfix[j]=ch;
j++;
}
ch=pop1();
}
else
{
while(ISPriority(stack1[top1])>=ICP(token))
{
ch=pop1();
/*Assigning the popped element into the postfix array. */
postfix[j]=ch;
j++;
}
push1(token);
}
i++;
token=infix[i];
}
while(top1!=0)
{
ch=pop1();
postfix[j]=ch;
j++;
}
postfix[j]='';
}
int ISPriority(char token)
{
switch(token)
{
case '(':return (0);
case ')':return (9);
case '+':return (7);
case '-':return (7);
case '*':return (8);
case '/':return (8);
case '?':return (0);
default: printf("Invalid expression");
break;
}
return 0;
}
/*Determining the priority of elements that are approaching towards the stack. */
int ICP(char token)
{
switch(token)
{
case '(':return (10);
case ')':return (9);
case '+':return (7);
case '-':return (7);
case '*':return (8);
case '/':return (8);
case '':return (0);
default: printf("Invalid expression");
break;
}
return 0;
}
/*Calculating the result of expression, which is converted in postfix notation. */
float eval(char p[], float x1)
{
float t1,t2,k,r;
int i=0,l;
l=strlen(p);
while(i<l)
{
if(p[i]=='x')
push(x1);
else
if(isdigit(p[i]))
{
k=p[i]-'0';
push(k);
}
else
{
t1=pop();
t2=pop();
switch(p[i])
{
case '+':k=t2+t1;
break;
case '-':k=t2-t1;
break;
case '*':k=t2*t1;
break;
case '/':k=t2/t1;
break;
default: printf(" Invalid expression");
break;
}
push(k);
}
i++;
}
if(top>0)
{
printf("You have entered the operands more than the operators");
exit(0);
}
else
{
r=pop();
return (r);
}
return 0;
}
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