3
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In the "Calculus" Apostol's Book in the part of the Integral of a Step Function

The first exercise: $\int_{-1}^{3}[x]dx$ where $[x]$ is the integer part of $x$ the result is 2. (page 70).

I could not get this result. I'm doing something wrong or simply don't understand the problem.

Could someone explain this, thanks.

  • 0
    Of cou$r$se "intege$r$ part" means floor. The term "floor" for this was invented by Iverson around 1960, while the Apsotol used the classic terminology of mathematicians.2012-05-27

2 Answers 2

5

I agree with you; the result should be 3, unless by "integer part", he means "floor". Just look at the two graphs:

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    I would assume he means floor function too.2012-05-25
1

Yes, Apostol means "the greatest integer function," [x], defined as the unique integer satisfying $x - 1 < [x] \le x.$ It is now usually referred to as the "floor function."