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I had thought that with the following two integrals, I was simply expressing the same idea in two different but equivalent ways, with the range of the values (excluding x) within the Floor[] term being, in both instances, in the interval [100,101). Nonetheless, they produce inconsistent results. In the first integral, the sum 100+T is in the interval [100,101) because of the assumptions about T :

Integrate[
 (Floor[100 + T + x])*PDF[NormalDistribution[0, sigma], x], {x, 2, 3},
 Assumptions -> {T \[Element] Reals, sigma \[Element] Reals, 
   sigma > 0, 0 <= T < 1}]

whereas in this second integral, T itself is in the interval [100,101)

Integrate[
 (Floor[T + x])*PDF[NormalDistribution[0, sigma], x], {x, 2, 3},
 Assumptions -> {T \[Element] Reals, sigma \[Element] Reals, 
   sigma > 0, 100 <= T < 101}]

Have I done something wrong or misunderstood something, or am I just being blind to an elementary mistake?

CrimsonDark
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1 Answers1

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MMA version 13.2

The first integral yields:

enter image description here

and the second one:

enter image description here

As you can see in the first integral T appears in: -3+T for 0<T<1 and in the second one:-103+T for 100<T<101. It is obvious that these are equivalent.

Daniel Huber
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    You've been kind enough to point out, *without actually saying so*, that (and I can only I plead tiredness!), I have been completely blind. I think if it had been me who was answering, I would have had a hard time NOT saying that. ....Thank you! – CrimsonDark Dec 30 '22 at 11:44
  • Don't worry, happens to all of us -;) – Daniel Huber Dec 30 '22 at 12:55