now this is like a book-written solution

Thanks a lot for it

since I have not used the method before I would like to ask a few more questions :P

1. The last step was (in a more generalised statement)

if a, and b are constants (or some constant intervalls) and a<b, then the integal I(f(x)) of the function f(x) converges, if:

a < I(f(x)) < b

question: if f(x) = sinx, I(sinx) = -cosx from 0 to some point in infinity, a = -2 and b = 2 the inequality:

-2 </= I(sinx) </= 2 ist true, but sinx does not converge. Why?

2. We carry back to my first problem, again the last step:

we had: integrals I_1 on [a;b] and I_2 on [c;d]

On which intervalls do we define the operations:

I_1+I_2

I_1*I_2

I_1^(I_2)

do se take the intersections or just perform the operations seperately for each pair of limits? (I assume the inverse operations will obey the same rules, if wring, correct me)

Thnaks again for the help,

best wishes, Marine