# C Program to implement Simpson method.

Write a C Program to implement Simpson method.
Simpson method is used for approximating integral of the function.
Simpson’s rule also corresponds to the 3-point Newton-Cotes quadrature rule.
In this program, We use the stack to implement the Simpson method. Read more about C Programming Language .

`/************************************************************ You can use all the programs on  www.c-program-example.com* for personal and learning purposes. For permissions to use the* programs for commercial purposes,* contact [email protected]* To find more C programs, do visit www.c-program-example.com* and browse!* *                      Happy Coding***********************************************************/#include<stdio.h>#include<conio.h>#include<math.h>char post_fix[80];float stack[80];char stack1[80];int top=-1,top1=-1;float eval(char post_fix[], float x1);void infix_post_fix(char infix[]);main(){        float x0, xn, h, s,e1,e2, e3;        char exp[80], arr[80];        int i,n,l=0;        clrscr();        printf("nEnter an expression: nn");        gets(exp);        puts("nnEnter x0, xn and number of sub-intervals: nn");        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_post_fix(arr);                e1=eval(post_fix,x0);                e2=eval(post_fix,xn);                e3=4*eval(post_fix, x0+h);                s=log(e1)+log(e2)+log(e3);                for (i=3;i<=n-1;i+=2)                s+=4*eval(post_fix,x0+i*h)+2*eval(post_fix, x0+(i-1)*h);            }        else        {                infix_post_fix(exp);                s=eval(post_fix,x0)+eval(post_fix,xn)+4*eval(post_fix, x0+h);                for (i=3;i<=n-1;i+=2)                s+=4*eval(post_fix,x0+i*h)+2*eval(post_fix, x0+(i-1)*h);            }        printf("nnThe value of integral is %6.3fn",(h/3)*s);        return(0);    }/*Inserting the operands in a stack. */void push(float item){        if(top==99)        {                printf("ntThe 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("ntThe stack is emptynt");                getch();            }        item=stack[top];        top–;        return (item);    }void push1(char item){        if(top1==79)        {                printf("ntThe 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("ntThe stack1 is emptynt");                getch();            }        item=stack1[top1];        top1–-;        return (item);    }/*Converting an infix expression to a postfix expression. */void infix_post_fix(char infix[]){        int i=0,j=0,k;        char ch;        char token;        for(i=0;i<79;i++)        post_fix[i]=' ';        push1('?');        i=0;        token=infix[i];        while(token!=")        {                if(isalnum(token))                {                        post_fix[j]=token;                        j++;                    }                else if(token=='(')                {                        push1('(');                    }                else if(token==')')                {                        while(stack1[top1]!='(')                        {                                ch=pop1();                                post_fix[j]=ch;                                j++;                            }                        ch=pop1();                    }                else                {                        while(ISPriority(stack1[top1])>=ICP(token))                        {                                ch=pop1();                                post_fix[j]=ch;                                j++;                            }                        push1(token);                    }                i++;                token=infix[i];            }        while(top1!=0)        {                ch=pop1();                post_fix[j]=ch;                j++;            }        post_fix[j]=";    }/*Determining the priority of elements that are placed inside the stack. */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("nnInvalid 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("nnInvalid 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("ntInvalid expression");                            }                        push(k);                    }                i++;            }        if(top>0)        {                printf("You have entered the operands more than the operatorsnn");                exit(0);            }        else        {                r=pop();                return (r);            }        return 0;    }`
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# C Program to implement Integration.

C Program to implement Integration. Integration is the important concept of calculus, which is the inverse of the differentiation. A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. Integration is used to find the area, volume of irregular shapes. In the following code, We find the integration of the defined function between two boundary limits, which are entered by the user. Read more about C Programming Language .

`/************************************************************ You can use all the programs on  www.c-program-example.com* for personal and learning purposes. For permissions to use the* programs for commercial purposes,* contact [email protected]* To find more C programs, do visit www.c-program-example.com* and browse!* *                      Happy Coding***********************************************************/#include <stdio.h>/* Propram to perform definite integration of a given function between two boundary limits input by user. Feel free to use and modify it, but please do not remove this comment. source: C for Engineering, http://c4engineering.hypermart.net */#define N 1000void main(void) { float i, a, b, sum = 0; printf(   "nThis program will integrate a function between two boundary limits."); printf("nnEnter the first boundary limit:"); scanf("%f", &a); printf("nEnter the second boundary limit:"); scanf("%f", &b); if (a > b) {  i = a;  a = b;  b = i; } for (i = a; i < b; i += (b - a) / N) {  /* Define your function below, and include the suitable header files */  y = x * x + 2 * x - 4;  sum += y * (b - a) / N; } printf("nnValue of integration is:%.3f", sum); getch(); return;}`
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