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A simple way to create “radiating waves” in Photoshop
There’s a technique I found about recently that I wanted to share with my readers. There is a simple way to create an impression of (...)
July 4, 2017 – Jakub Marian – Visual arts
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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
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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
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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
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Derivative of $x^x$
Calculating the derivative of $x^x$ is a very simple task, but it may be hard to find the general idea on your own, so here it is. We will (...)
July 2, 2017 – Jakub Marian – Mathematics
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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:
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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
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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
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Correlatives in Esperanto
In the grammar of Esperanto, words like “where”, “there”, “somewhere”, “when”, “then”, “sometime”, etc., are called correlatives. (...)
June 27, 2017 – Jakub Marian – Esperanto
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‘June’ in European languages
The English name “June” comes from Latin iunius, the month of the Roman goddess Iuno (usually spelled “Juno” in English), who was the (...)
June 7, 2017 – Jakub Marian – Maps
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Gold reserves of national central banks per capita in Europe
Most national central banks in Europe hold a large amount of reserves in the form of foreign banknotes and deposits, treasury bills, gold, (...)
May 28, 2017 – Jakub Marian – Maps
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