8) Riemann-Integral, student package, rightsum, rightbox, middlesum, leftsum    [09.txt]
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> with(student);
> ?middlesum
> ?rightsum
> ?leftsum
Nochmals zu Uebung 2, Aufgabe 4 b):
(i):
> rightsum(1/(1+x^2),x=0..1);
> eval(%);
> simplify(%);
> evalf(%);
> n:=4:evalf(n*sum(1/(j^2+n^2),j=1..n));;
> n:='n':
> rightsum(1/(1+x^2),x=0..1,n);
> limit(%,n=infinity);
> ?rightbox
> rightbox(1/(1+x^2),x=0..1);
> rightbox(1/(1+x^2),x=0..1,15);
> leftbox(1/(1+x^2),x=0..1,15);
> middlebox(1/(1+x^2),x=0..1,15);
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(ii):
> rightsum(1/(x+1),x=0..1);
> evalf(%);
> n:=4:sum(1/(j+n),j=1..n);n:='n':
> evalf(%%);
> rightsum(1/(x+1),x=0..1,n);
> limit(%,n=infinity);
> rightbox(1/(x+1),x=0..1,15);
>