What is real GDP and GDP growth?
Politicians and economist always keep talking about gross domestic product (or GDP for short). But what is GDP and why does everybody seem (...)
November 15, 2018 – Jakub Marian – Economics

How to understand GDP indicators
Gross domestic product, or GDP for short, is perhaps the single most important measure in modern macroeconomics. That is not to say that (...)
November 5, 2017 – Jakub Marian – Economics

GDP of Arab League Countries 2016
The Arab League is a regional organization of 22 countries where (a dialect of) the Arabic language is spoken. The following table shows (...)
October 26, 2017 – Jakub Marian – Economics

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

I will send you one of my ebooks for free as a little gift.
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

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

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 buying my ebooks and prints.
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
