# Author Archives

## Angelo Napolitano

I love nature, problems, formulas, making calculations, evaluating integrals, performing experiments, cooking. I am full of imagination and creativity, very sensitive, empathetic and, although a bit introvert at first, I love making friends. To this, add my love for music and you get "Angelo"! I absolutely love Charlie Puth, my favourite singer! And I love singing and playing the piano!

## Voltage and current | What are they?

Voltage and current are two very important quantities that we want to monitor in circuits to exactly know what’s going on. But what are they, and what is the difference… Read more Voltage and current | What are they?

## Integral of xln(x)

In this post I am going to explain step-by-step how to integrate the function xln(x). We can solve it by using integration by parts (click here if you want to… Read more Integral of xln(x)

## Integral of sec²(x)|Two ways

Hi everyone! I know it’s been a really long time since my last post, but lessons during COVID-19 really had me busy and stressed out… but here I am again!… Read more Integral of sec²(x)|Two ways

## Definite double integral of sin(y²)

I’ll be honest: I had no idea how to do this at first, but then I thought that it was probably easier than I could imagine. What most likely blocks… Read more Definite double integral of sin(y²)

## Integral of ln²(x)

In this post I will show you how to find the anti-derivative of the function f(x)=ln²(x). We are going to use integration by parts: Now we can write u times… Read more Integral of ln²(x)

## Integral with summations inside

I am a big fan of blackpenredpen. This guy posts videos on Youtube about calculus and more. Some days ago I received a notification and this is what the thumbnail… Read more Integral with summations inside

## i-th root of i

In my previous post we talked about i^i and we evaluated it. We found that the result is a real number, although you would expect it to be complex since i is an imaginary number. Is this the case for the i-th root of i? First of all, let’s write this as a power: Now, this is can also be written as We already know what i^i equals therefore, This means it’s simply the inverse of i^i, and so it’s a real number as well! If you use a calculator… Read more i-th root of i