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I'm totally stuck with that, i don't know where to start.

I have to Integrate a function between a and b with n intervals in C.

I only have the function definition :

float funcintegrate(float (*f)(float x), float a, float b, int n);

I need to use the trapezoidal method.

EDIT :

Thanks all for you tips. I have now the answer !

Numerically integrate the function in the interval [a, b] using trapezoidal method (or rule) :

float funcintegrate(float (*f)(float x), float a, float b, int n);

int i;
double x;
double k = (b - a) / n;
double s = 0.5 * (f(a) + f(b));

    for (i = 1; i < n; i++) {
         x = a + k * i;
         s = s + f(x);
    }

return s * k;

}
TheTime
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    Please show us what you have tried before asking for help. Is this a homework? If it is, please add a tag. – Sergey Kalinichenko Dec 18 '11 at 15:54
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    Try Numerical Recipes in C (it is freely available) for numerous integration implementations. – Omar Dec 18 '11 at 15:55
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    Don't use `float` when `double` is suitable. – pmg Dec 18 '11 at 15:57
  • @pmg i can't change function definition. I must use the one i gave above. – TheTime Dec 18 '11 at 15:59
  • @dasblinkenlight In fact, i don't really understand this notation : float (*f)(float x) – TheTime Dec 18 '11 at 16:01
  • @TheTime: see this recent question and answer: http://stackoverflow.com/questions/8552682/function-arguments-in-c – pmg Dec 18 '11 at 16:02
  • Do you know what integration is? – detly Dec 18 '11 at 16:02
  • @detly I just don't know how to make that in C – TheTime Dec 18 '11 at 16:03
  • @TheTime - yep, just clarifying the scope :) – detly Dec 18 '11 at 16:04
  • For notation, google 'function pointers in C*. There are various methods to numerically integrate (which can also be googled), e.g., upper or lower sum approximations which you are most likely to use as they are easy. There are for sure good pseudo algorithms to be googled. – gnometorule Dec 18 '11 at 16:05
  • ...and the function pointer is used to pick whichever numerical method you actually implemented. – gnometorule Dec 18 '11 at 16:05
  • @TheTime look up "function pointers" in C. Long story short, you can call a function passed in to you indirectly, like this: `f(1.23)`. `f` is not the name of a function, but the name of your first parameter. – Sergey Kalinichenko Dec 18 '11 at 16:06
  • @TheTime: `float (*f)(float x)` declares `f` as a pointer to a function that takes a single float parameter and returns a float. You can call it as you would a normal function, such as `result = f(x);`. – John Bode Dec 18 '11 at 16:11

1 Answers1

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Your funcintegrate() function should basically divide the [a, b] interval into n subintervals, calculate the value of f() on all subinterval endpoints, then use them to compute a value of certain expression for each of the subintervals and finally add up all the values of that expression.

The subexpression to calculate in each iteration depends on the particular numerical integration method you have chosen and impacts performance and accuracy trade-off.

In the simplest case the expression is the product of the value of f() at one of the endpoints multiplied by the length of the subinterval. This corresponds to "bar-chart approximation" to the field under the curve. It is very inaccurate and once you successfully implement it you should try more complex methods.

These two wikipedia articles give a good description of a number of different methods each sharing the general algorithm I described above: Euler method, Runge-Kutta methods.

I also recommend reading relevant chapters in "Numerical Recipes in C".

EDIT: Trapezoidal method uses for each subinterval an expression which represents the area of a trapezoid which is based on the subinterval and extends upwards (or downwards depending on the sign of f()) until its vertical sides cross the curve. The two intersection points are their connected with a straight line (which is where approximation is made since f() may not be straight between the points).

Adam Zalcman
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