(* ::Package:: *)

(*
  Rechnernutzung in der Physik, Wintersemester 2023/24
  Allgemeine Trapez-Regel
*)


(* F_TR^(N) *)

Trapez[fkt_,aa_,bb_,nn_] := Module[
    {sum=fkt[aa],hh=(bb-aa)/nn,i},
    For[i=1,i<nn,i++,
      sum=sum+2*fkt[aa+i*hh];
    ];
    sum=sum+fkt[bb];
    sum=hh/2*sum;
    Return[sum];];



f1[x_] := Exp[-(x+2)^2] + Exp[-x^2];
a1 = -5.;
b1 = 3;


Trapez[f1,a1,b1,60]


nmax = 5
lsttrapez = Table[ {n,Trapez[f1,a1,b1,n]},{n,2,nmax}]
resnint = NIntegrate[f1[x],{x,a1,b1}]
lstnint = Map[{#,resnint}&,Table[n,{n,2,nmax}]]

(lsttrapez - lstnint) / resnint

ListPlot[ {lsttrapez,lstnint}, Joined->{False,True},PlotRange->All]