 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 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 Do certain numbers in a lottery have a higher probability of winning than others? Does going for “nice” sequences of numbers, like 1 2 3 4 5 6, reduce the probability of winning in a lottery? Some people think so. “Have (...) September 25, 2014 – Jakub Marian – Mathematics Will computers ever be smarter than humans? When I was a child, I was fascinated by the idea that some day we will be able to construct computers that will be smarter than us. Later, (...) September 12, 2014 – Jakub Marian – Mathematics Arithmetics in which you can divide by zero When I was still in primary school, I was fascinated by things you “can’t do” in mathematics and developed a “theory” of division by zero. (...) June 8, 2014 – Jakub Marian – Mathematics Is it possible to divide by zero? This is a common question on mathematical discussion boards, with people sometimes feeling that mathematicians are too closed-minded for (...) June 7, 2014 – Jakub Marian – Mathematics