Mathematics

 What it’s like to work as a data scientist in a bank I’ve been working as a data scientist in the private sector (in a bank) for the past three years, one year as the leader of a chapter of (...) January 23, 2022 – Jakub Marian – Mathematics
 What is $0^0$ ($0$ to the power $0$)? A short answer to this question is that $0^0$ is usually left undefined in introductory calculus classes, just like $0/0$, but it is often (...) October 15, 2017 – Jakub Marian – Mathematics
 Integral of $\cot(x)$ To integrate cot(x), recall that cot(x) = cos(x)/sin(x), so ∫ cot(x) dx = ∫ cos(x)/sin(x) dx. (...) September 21, 2017 – Jakub Marian – Mathematics
 Integral of $\sin(x)\cos(x)$ The function $\sin(x)\cos(x)$ is one of the easiest functions to integrate. All you need to do is to use a simple substitution $u = (...) September 6, 2017 – Jakub Marian – Mathematics  How to calculate the factorial of 1/2 As I proved in my article on integration by parts (at the end), the factorial of a natural number$n$can be calculated using the (...) July 8, 2017 – Jakub Marian – Mathematics By the way, have you already seen my brand new web app for non-native speakers of English? It's based on reading texts and learning by having all meanings, pronunciations, grammar forms etc. easily accessible. It looks like this:  Integral of$\log(x)$(or$\ln(x)$) The natural (base$e$) logarithm is usually denoted$\log(x)$in mathematics, but for the sake of students of other disciplines, we will (...) July 7, 2017 – Jakub Marian – Mathematics  Explanation of integration by parts Integration by parts is one of the first methods people learn in calculus courses. Together with integration by substitution, it will (...) July 6, 2017 – Jakub Marian – Mathematics  Integral of$\sin^3(x)$Integrating the third power of$\sin(x)$(or any odd power, for that matter), is an easy task (unlike$∫ \sin^2(x)\,dx$, which requires (...) July 4, 2017 – Jakub Marian – Mathematics A small but necessary interruption: This website does not contain any ads and is completely dependent on the support of its readers. If you enjoy reading articles here, please, consider helping by using my web app for English learners.  Integral of$\sin^2(x)$The integral can be calculated using integration by parts (using the formula$∫u’(x)v(x)\,dx = u(x)v(x) - ∫ u(x)v’(x)\,dx$). Let’s (...) July 3, 2017 – Jakub Marian – Mathematics  Integral of$\tan(x)$The easiest way to integrate$\tan(x)$is to recall that$\tan(x) = \frac{\sin(x)}{\cos(x)}$. Do you see the necessary substitution? By choosing$y = \cos(x)$, that is,$dy = -\sin(x)\,dx\$ (...) July 2, 2017 – Jakub Marian – Mathematics