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Trapezium rule

  1. Nov 7, 2015 #1
    This is not giving me the right answer! I have checked for errors like integer division and rounding, but can't find any. I am aware the comments are slightly inaccurate and they will be improved. But what's wrong with the actual code?
    Code (Java):

    //This method uses the trapezium rule to calculate the integral
       //a is the lower limit, b the upper limit, c is the power of x in the function, N the number of trapezia
       //Returns the result of the integral
       public static double trapeziumRule(double a, double b, double c, int N){

         double h = (b-a)/(N-1);             //h is the width of a single trapezium
         double x = 0.5*(f(a,c)+f(b,c));           //x is the average height of the trapezium
         for(int i=2; i<N-1; i++){

           x += f(a+h*i,c);
         }
         double integral = h*x;
         return integral;
    It's probably something in the actual maths... should i run from 2 to N-2? I clearly don't know how to use sum notation properly, since I can't convert ##\sum_{i=2}^{N-1}## into a for statement correctly.

    Actually, is that the problem? Should it be i<=N-1? And i starts from 1? That would also affect my formula for h.

    Except that doesn't work either.
     
    Last edited: Nov 7, 2015
  2. jcsd
  3. Nov 7, 2015 #2
    Whoops, found the flaw. Difference in the meaning of N in my course notes and the meaning of N in my code!
     
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