Help please

[missmango]

Please help me I have to write a program that use the trapezoidal rule for integration
f(x)= x^2.

The following is my code, but I get stuck when writing for define area.

#include <iostream>
#include <cmath>
using namespace std;

double trapezoid(int n, double a, double b);
// This function will take three arguments: the number of intervals, the limits and return the value of the definite integral.

int main()
{
	char yesno='y';
	while(yesno=='Y' || yesno=='y')
	{
		
		double area, h, a, b;
		int n;
		
		cout<< "Enter the lower and upper limits of the interval: \n";
		cin>>a>>b;
		cout << "Enter the number of intervals: \n";
		cin>>n;
		
		cout<< "The area under the curve (intergrall) is: \n";
		cin>> trapezoid>>endl;
		
	
	cout<<"continue? (y or n) \n";
	cin>>yesno; 
		
	} 



}


double trapezoid(int n, double a, double b)
{
	double h
	
	double h = ( ( b - a ) / n );
    double y = 0;
    double sum = 0;
 
    for ( int i = 0; i <= n; i ++ )
    {
        y += h;
        sum = sum + // dont know what have to write for f(x)= x*x;
    }
    sum = sum * ( h / 2 );
 
    return sum;


}

[giblit]

You can simply put x * x

or if sum is the thing you are trying to square you can simply do:

sum *= sum;
//or
sum = sum * sum;

Also it would be impossible to input into a newline. (line 23 remove endl)

[missmango]

sum is not the thing I try to square.
I change x*x to x * x and take out line 23 but the program still some error that I cant run.

[Disch]

sum is not the thing I try to square.

So then what are you trying to square?

but the program still some error that I cant run.

It helps if you tell us what the error is.

[giblit]

well um you are supposed to replace x with some variable otherwise that would be like trying to do ??? * ??? What exactly are you trying to square? Also I didn't mean remove line 23 completely I meant remove the endl on line 23.

[condor]

missmango wrote:

I get stuck when writing for define area.

Indeed, you are wrong when define area of an elementary trapezoid. The area is:

area = medium_lineLength * trapezoid_height

so please calculate the two values and all wil be OK.

[condor]

As an example (you have to extract the trapezoid function!)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

#include <iostream> int main(){ double a, b, h, sum = 0.; double x1, x2, median; double area; int n; std::cout << "Enter the ends of the interval [a, b] : \n"; std::cout << "a = "; std::cin >> a; std::cout << "b = "; std::cin >> b; if(b < a) return 1; std::cout << "Number of subintervals of [a, b]? "; std::cin >> n; // The length of a subinterval h = (b - a) / n; for(int i = 0; i < n; ++i){ x1 = a + i * h; // abscissa of the left end x2 = x1 + h; // abscissa of the right end // For the function f(x) = x^2 we have median = (x1 * x1 + x2 * x2) * .5; // The area of each trapezoid area = median * h; // The area under the curve sum += area; } std::cout << "Approx. area = " << sum << '\n'; std::cout << "Exact area = " << (b * b * b - a * a * a) / 3. << '\n'; return 0; }

Example 1 ********** Enter the ends of the interval [a, b] : a = 0 b = 4 Number of subintervals of [a, b]? 10 Approx. area = 21.44 Exact area = 21.3333 Example 2 ********** Enter the ends of the interval [a, b] : a = 0 b = 4 Number of subintervals of [a, b]? 100 Approx. area = 21.3344 Exact area = 21.3333 Example 3 ********** Enter the ends of the interval [a, b] : a = 0 b = 4 Number of subintervals of [a, b]? 1000 Approx. area = 21.3333 Exact area = 21.3333