[SOLVED] Integrate a function between a and b

[newe12]

Hi!

I want to integrate a function between the lower boundary "a" and the upper boundary "b".

I have got:

header.h:
inline double integrate(double(*f)(double), double a, double b)
{
    double sum = 0;
    double n = 20;
    double result = (b-a)/n;
    for (double k = 1.; k < n-1; k+=1.)
    sum += f(a + k*result);
    return result * ((f(a) + f(b)) / 2 + sum);
}
///
and in mainwindow.cpp (in the void function):
          double cp = lineEdit->text().toDouble(&ok);
          double x;
          double a=.025;
          double b=.075;
          double function=1-(cp*(1-x)); 
          double integrateresult = integrate(function, a, b);

But it does not integrate the function...

Does someone see the mistake?
Please share!
Thanks in advance!

[Chris Kawa]

integrate() expects a pointer to function and you are giving it a double called "function". Naming a variable "function" does not make it a function :)

In this code "function" variable is not a function. It's a variable of type double and undefined value (undefined because you never gave value to x so the result is garbage).

[newe12]

Hello @Chris-Kawa !

Thanks for pointing out some problems.

I have done some improvements and the following code compiles without any problem:
in the header-file:

inline double f(double x)
{
     return x*x;
}

in mainwindow.cpp in the function which is emitted with a QPushButton:

            double aB = .1;
            double bB = 2;
            int n = 10000;
            double h = (bB-aB)/n;
            double area = (f(aB)+f(bB))/2;

            for (int i=1;i<n;i++)
            {
                area += f(aB+i*h);
            }
            QString resultString = "";
            lineEdit->setText(resultString.setNum(area));

Furthermore, it even calculates the "area" and gives the result "14033.3". This is unrealistically high and incorrect!

Mathematica gives me for the integration of the same equation:
integral_0.1^2 x^2 dx = 2.66633
which is correct!

If someone has a helpful idea, please share!

[newe12]

Solved!

area = area*h; 

was missing after the for-loop!

Now the result is: 2.66633
the same is with Mathematica: 2.66633
(For math-friends: at least approximately, if not "too" many digits are compared; Nevertheless setting "n" from "n=10000" to a higher accuracy, the area will be approximated more correctly!)

Thanks anyway! :-)

[KiwiJeff]

@newe12 said:

double h = (bB-aB)/n;
double area = (f(aB)+f(bB))/2;

What is h for?
And why are you starting the area with the average value of the two boundary points?

Shouldn't it be more like:

 area += f(interval*i)

where i goes from boundary to boundary and interval is .1?