Integrating: MathsJamJam

This weekend, I attended the MathsJam annual gathering. It was a wonderful event full of brilliant talks, great competitions, and a fantastic game of mathematical Jeopardy. On particular highlight though, was MathsJamJam.

When MathsJam is in person, people bring their instruments and have a sing along to songs from the ever-evolving MathsJamJam song book. Songs which you may well know, but with lyrics changed to be about maths. This year audio and video were sent in instead, which people could sing along to.

I submitted my own set of lyrics to Levitating by Dua Lipa. Alas, I don’t have the recording but can at least share the lyrics!

Integrating 

Lyrics by Sophie Maclean
To the tune of Levitating by Dua Lipa

Backing track: https://www.youtube.com/watch?v=nK9hD9_SAdU

If you wanna find an area, beneath a curve or line
I got a method you should know
I have some mathematics that is full of lots of cool tricks
And it’s this that I have brought to show
Newton did it first? Leibniz did it first?
That debate goes too and fro
Doesn’t matter either way it’s what I’m teaching you today
It’s calculus come on let’s go

You want A? I want A baby:
The area, I’m integrating
I’m anti-diff, -erentiating
Yeah-yeah-yeah-yeah

I got two lim-its, it’s def-inite
Meaning you are not meant to add the c
I’m integrating 
(In) lieu (of) limi-its: inde-finite
And so you, must be, sure to add the c
I’m integrating 

(To) show you how we integrate I first want to approximate, 
The area beneath our curve
Split it into rectangles and sum the areas of those
Now tell me what you can observe
Make the rectangles, infinitely small
Use more so the width’s conserved
Tending to infinity, the limit of the sum will be 
The area, just hold your nerve

You want A? I want A baby:
The area, I’m integrating
I’m anti-diff, -erentiating
Yeah-yeah-yeah-yeah

I got two lim-its, it’s def-inite
Meaning you are not meant to add the c
I’m integrating 
In lieu (of) limi-its: inde-finite
And so you, must be, sure to add the c
I’m integrating 

(*beat*) An uncountable infinity
You can sum across it easily 
Addition continuously
(Yeah-yeah-yeah-yeah)
I’m integrating (woo)
You can integrate things with respect
To the variable you select
To the y axis or the x
Yeah-yeah-yeah-yeah (woo)

Let’s take a polynomial degree n
We integrate so change the coefficients
And the solution we get will be then 
deg, ree, n, plus, one
Or start with a trig function, how about sine?
Integrate to find what’s beneath the line 
In this case the answer’s minus cosine
And ,co- sine, gives, sine

You want A? I want A baby:
The area, I’m integrating
I’m anti-diff, -erentiating

With the two lim-its, it’s def-inite
Meaning you are not meant to add the c
I’m integrating (woo)
(*beat*) An uncountable infinity 
You can sum across it easily 
Addition continuously 
I’m integrating (woo)
You can integrate things with respect
To the variable you select
To the y axis or the x
Yeah-yeah-yeah-yeah 

With the two lim-its, it’s def-inite
Meaning you are not meant to add the c
I’m integrating 
In lieu (of) limi-its: inde-finite
And so you, must be, sure to add the c
I’m integrating  

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