Answer to Question #335710 in C++ for Suchperson

Question

The Rectangular Rule A. The rectangular rule (also called the midpoint rule) is perhaps the simplest of the three methods for estimating an integral. i. Integrate over an interval a ≤ x ≤ b. ii. Divide this interval up into n equal subintervals of length h = (b − a)/n. iii.Approximate f in each subinterval by f(x*j ), where x*j is the midpoint of the subinterval. iv. Area of each rectangle: f(x*j)h, f(x*j)h,. . . , f(x*n)h. The approximation on the RHS becomes more accurate as more rectangles are used. In fact, You are required to: v. write pseudocode algorithm to determine the integral of a function between two specified points using the rectangular rule. vi. write C++ computer programs to determine the integral of a function between two specified points using the rectangular rule.

Answer 1

#include<iostream>
#include<cmath>
#include<iomanip>

using namespace std;

double approx(double x)
{
	return (6 * pow(x, 4) - 7 * pow(x, 3)+4*x);
}

int main()
{
	double a, b;
	int n;
	cout << "Please, enter lower limit: ";
	cin >> a;
	cout << "Please, enter higher limit: ";
	cin >> b;
	cout << "Please, the number of rectangles: ";
	cin >> n;
	double s = (approx(a) + approx(b)) / 2;
	double h = (b - a) / n;
	for (int i = 1; i <= n-1; i++)
	{
		s += approx(a + i*h);
	}
	double I = h*s;
	cout << setprecision(10) << I << endl;
}