# Mathematics

 Integral of $x^n$ How to calculate the indefinite integral of $x^n$? It’s quite simple. We are looking for a function $f(x)$ such that $f’(x) = x^n$. As you (...) July 2, 2017 – Jakub Marian – Mathematics
 Integral of $e^{-x^2}$ from $-\infty$ to $\infty$ In this article, I will give a detailed explanation of why the Gaussian integral is equal to $√\pi$, that is, why the following equality (...) June 29, 2017 – Jakub Marian – Mathematics
 The ‘day of the week boy or girl’ paradox explained There is a well-known result in probability theory that seems to defy common sense. Note that in the problem statement we assume that the (...) July 25, 2016 – Jakub Marian – Mathematics
 Labelling articles as “per capita” when the unit used is different After I published my recent article about the Number of metal bands per capita in Europe, I got quite a few comments saying that my use of (...) May 29, 2016 – Jakub Marian – Mathematics
 What does it mean for a function to be well-defined? A common addendum to a formula defining a function in mathematical texts is, “it remains to be shown that the function is well defined.” (...) March 3, 2015 – Jakub Marian – Mathematics

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 Is 0.999… (repeating) equal to 1? The short answer is yes. $0.\bar 9$ (zero point 9 repeating) is exactly 1. However, a lot of people find this result counter-intuitive (...) October 16, 2014 – Jakub Marian – Mathematics