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Featured
Contents
- 1 My First Blog Post
- 2 Voltage and current | What are they?
- 3 Integral of xln(x)
- 4 Integral of sec²(x)|Two ways
- 5 Integral of 1/sqrt(e^x-1) from ln(2) to infinity
- 6 Definite double integral of sin(y²)
- 7 Integral of ln²(x)
- 8 Integral with summations inside
- 9 i-th root of i
- 10 i to the i-th power
- 11 Hard looking yet beautiful integral
- 12 Gaussian integral using Feynman’s technique
- 13 Integral of e^-x^t using Feynman’s technique
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?
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
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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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