- #1
martizzle
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Problem 51 from GRE math test practice book or test form code: GR0568
The problem is as follows (ps. I'm sorry, I do not have LaTeX or something)
If |_ x _| denotes the greatest integer not exceeding x, then 'the integral from zero to infinity' of |_ x _| * e ^ (-x) dx = ?
The answer is 1/(e - 1)
I thought that the way to solve the problem would be:
1. the limit of |_ x _| and x, as x -> infinity, is x.
2. integrate x * e ^ (-x)
3. plug in the limits, to get the answer
But this method gives me 1
Please help, and sorry for the problem description (not using LaTeX/etc)