Answer to Question #241755 in C++ for HelloWorld

Question

Write the C++ program that will compute for the area under the curve of the equation,

Input:

- The lower limit a.

- The upper limit b.

- The number of trapezoids.

Compute for the area using trapezoids:

- Declare an array whose size will be equal to the number of trapezoids.

- Use a looping structure.

- Pass arguments to a module that will compute for the area of the trapezoid and return the area back to the calling method.

- Each element in the array will be assigned the returned area for every trapezoid.

- Use an accumulator to compound the sum of each element in the array. 

Compute for the area using integral:

- Pass arguments to a module that will compute for the area under the curve and return the area back to the calling method.

- Assign the returned area to a variable.

Output:

- The area of each trapezoid.

- The area using the trapezoid method.

- The area using integral calculus.

- Percentage error (absolute).

Answer 1

#include<iostream>
using namespace std;
	
float y(float x)
{
   
    return 1/(1+x*x);
}
 
float trapezoidal(float a, float b, float n)
{
    
    float h = (b-a)/n;
 
    
    float p = y(a)+y(b);
    for (int i = 1; i < n; i++)
        p += 2*y(a+i*h);
 
    return (h/2)*p;
}
double Area(int a1, int a2,
                    int h)
{
    return ((a1 + a2) / 2) * h;
}
int main()
{
    int base1,base2,height;
	cout<<"Input the lower limit a: ";
	cin>>base1;
	cout<<"Input the upper limit b: ";
	cin>>base2;
	cout<<"Enter the number of trapezoids: ";
	cin>>height;
	double area = Area(base1, base2,
                            height);
    cout << "Area of each trapezoid is: " << area;
    float x0 = base1;
    float xn = base2;
    int n = height;
    float percentage=(trapezoidal(x0,xn,n)/area)*100;
    cout<<"\nArea using trapezoidal method is: "<<trapezoidal(x0, xn, n);
    cout<<"\nArea using integral calculus is: "<<area;
    cout<<"\nThe percentage is: "<<percentage;
    return 0;
}