Numerical Integration using the 'standard' methods:

Left End, Right End, Midpoint, Trapezoid Rule, Simpsons Rule.





        Sidney Birnbaum, Mathematics Department

        California State Polytechnic University, Pomona

        3801 West Temple

        Pomona, Ca   91768



        SBirnbaum@CsuPomona.edu



In addition to performing the indicated calculations, the

program offers the option of doubling N, the number of

subintervals, and recomputing.



    Input variables

A, B    left, right endpoints of the interval of integration.

N       number of subintervals.

f(x)    function to be integrated. [note lower case x]



    Output Variables

LE      Left End estimate: H*Sum(f(x[i]),i,0,N-1) .

RE      Right End estimate: H*Sum(f(x[i]),i,1,N) .

TR      Trapezoid rule estimate: (LE + RE)/2  .

MD      Midpoint rule estimate: H*Sum(f(x[j]),j,1,N);

        x[j] is the midpoint of the jth subinterval.

SI      Simpsons rule estimate; calculated only for N even.



    Principle Internal Variables

H       (B-A)/N  : subinterval length.

FA      f(A) : value of f at left end; f(x[0]).

FB      f(B) : value of f at right end; f(x[N]).

w       current value of x[i] .

SE      Sum(f(x[i]), for i even; end points not included.

SO      Sum(f(x[i]), for i odd;  end points not included.

SM      Sum(f(x[j])), x[j] is the midpoint of the jth interval.



When N is doubled:

2N\->\N : H/2\->\H

SO+SE\->\SE

SM\->\SO

and only SM need be recomputed.