# Home

Welcome to Add just a bit of pi!

• ## My First Blog Post

28 September 2019

Be yourself; Everyone else is already taken. — Oscar Wilde. Hello everyone! My name is Angelo, I am 16 and I have been into the world of science since I was a kid, when I used to look at my dad making some project with his soldering iron. Always searching for an answer to my why’s, never satisfied and longing to know more. You know, I used to be terrible at maths when I was in elementary school. My teacher was aware of my potential and just wouldn’t let me… Read more

• ## Voltage and current | What are they?

7 October 2021

Table of Contents VoltageElectron flowOvervoltage | EffectsCurrentConventional current flowKirchhoff’s current lawVoltage and current | Differences and relationshipElectric resistance and Ohm’s LawsFirst Ohm’s lawElectric resistivity | Second Ohm’s lawJoule’s effectVoltage and… Read more

• ## Integral of xln(x)

14 September 2021

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 sec²(x)|Two ways

28 June 2020

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 1/sqrt(e^x-1) from ln(2) to infinity

28 April 2020

Hi guys! Hope you are all doing well in these days of quarantine which is hopefully ending soon. I like to spend my time integrating and watching videos about calculus… Read more

• ## Definite double integral of sin(y²)

20 April 2020

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

• ## Integral of ln²(x)

15 April 2020

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 with summations inside

14 April 2020

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

• ## i-th root of i

8 March 2020

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 to the i-th power

8 March 2020

Ever wondered what the imaginary unit i raised to itself is equal to? Is it going to be a complex number? Or a real one? Let’s find out! Let’s first define i: Therefore, There is an identity in maths which is in my opinion one of the most beautiful equations that exist, and that is Euler’s identity: This means At this point we have two expressions: We can use the second one to replace the -1 in the first: We no longer have the i because i times i equals… Read more

• ## Hard looking yet beautiful integral

7 February 2020

Never judge a book by its cover: this is the case. This integral requires a bit of work and knowledge, as you need to know about the Gaussian integral (I… Read more

• ## Gaussian integral using Feynman’s technique

6 January 2020

In my last post we evaluated the following definite integral This is the formula we got: and this is the integral we want to evaluate: which is equivalent to because… Read more

• ## Integral of e^-x^t using Feynman’s technique

5 January 2020

Wouldn’t it be nice to generalize the Gaussian integral to any exponent of –x? This is the famous integral: Since this is an even function, it can be written as… Read more

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