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Welcome to Add just a bit of pi!
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Featured
My First Blog Post
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
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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
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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
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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
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Integral of 1/sqrt(e^x-1) from ln(2) to infinity
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
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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
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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
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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
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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
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i to the i-th power
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
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Hard looking yet beautiful integral
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
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Gaussian integral using Feynman’s technique
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
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Integral of e^-x^t using Feynman’s technique
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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Add just a bit of pi 