Question

write a program to approximate the integral of a function of one variable. Your program will use the trapezoid rule.

Test your program using the following functions:

Integral of 1/x from 1 to 2

Integral of x2sin(x) from -1 to 1

Integral of x2e2x from 0 to 3

Answer 1

#include <stdio.h>    #include <conio.h>  #include <math.h>#define f(x) (1/x)   //use macros to define the integrand//#define f(x) ((x)*(x)*sin(x))  //#define f(x) ((x)*(x)*Exp(2*(x)))  //uncoment to change integranddouble calcAreaTrap(double a1, double b1){     //function calculates the area of trapezoid of height b1-a1 , and the center line f((a1+b1)/2).return (b1-a1)*(f(a1)+f(b1))/2;}             // or this function return the approximation value between two end points a1 and b1 , based on the trapezoid methoddouble calcArea(double A, double B,int N)  // this function will return approximation value between two end points,a and b, based on the method specified by flag{   double buf = 0;                        // Declaration and initialization  of the auxiliary variable tha will be contain approximation value between two points , a and b   double h = (B-A)/N;                    //Declaration and initialization  of the auxiliary variable tha will be contain value of space step , h = b1-a1   //this part will calculate approximation value between two end points   for (int i =0;i<N;i++) {   buf=buf+calcAreaTrap(A+i*h,A+i*h+h);   }      return buf;}void OutPut(double Area){       //this function type on the screen area's value   printf("The integral's value is : %f", Area);   }int main(int argc, char *argv[]){OutPut(calcArea(1,3,1000));// by using all define function program will calculate and output approximated value of the integral of the function f(x) tha define in head by macros in interval (0;3) with space step 0.03getch();return 0;}