Zusammengesetzte Simpson'schen Regelrestart : Digits:=8;

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n:= 8; # Teilintervalle

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Simpson:=proc( f , a , b , n ) local j,h,S; h:=(b-a)/n ; S:= evalf(h/3* (f(a)+f(b)+2*sum(f(a+2*j*h), j=1..(n/2)-1) + 4*sum(f(a+(2*j-1)*h), j=1..(n/2)) ) ) ; end proc:f:=(x) -> x*ln(x): a:= 1: b:= 2: h:= (b-a)/n;

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plot( diff(f(x), x$4) , x=a..b );

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Integ:=Simpson(f,a,b,n);

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Tat_Integ:= evalf( int(f(x), x=a..b) );

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Fehler_Schranke:=evalf(eval( diff(f(x), x$4) , x=1 )*(b-a)/180*h^4 );

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Tat_Fehler:= Tat_Integ - Integ ;

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