An interesting integral appeared on a test that I took today. I had no idea how to solve it, and was wondering if any of you all could possibly help me(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int_{0}^{1} \frac{1}{x}-floor(\frac{1}{x})

[/tex]

we first had to draw the graph from 0 to 1, (which has a max of 1, a min of 0 (at 1/n for any integer n), with a negative slope at all points (more or less).

then we had to describe the integrability...

and finally, we were asked to evaluate the integral, noting that

[tex]

\gamma = \lim_{n->\infty} \sum_{n=1}^{\infty} \frac{1}{n} - \ln (n)

[/tex]

I had no idea on what to do from here (besides the fact that there was probably going to be a substitution involving 1/x, so that the limits of integration are changed to 1-> infty)...

~dazed and confused

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Interesting integral

**Physics Forums | Science Articles, Homework Help, Discussion**