Calculus Rhapsody

Описание: Calculus Rhapsody
By Phil Kirk & Mike Gospel
(Lyrics below)

We've had this little school project of ours here on YouTube for over 10 years!! It's been so lovely seeing all of your nice comments over the years. We've updated this description to show you what we're up to nowadays (we're both adults with jobs now!). You can find us online at the links below. Thanks everyone!

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Follow Mike:
Mike's podcast "How Star Wars Is It?": https://podcasts.apple.com/us/podcast...
HSWII Instagram:   / howstarwarsisit  
HSWII Twitter:   / howstarwarsisit  
Mike's art and face: https://www.instagram.com/wordgospel0...
Mike's Twitter: https://twitter.com/mikegospel?lang=en

Follow Phil:
Indy Rustic: https://www.indyrustic.com/
Plat Collective Instagram:   / phil_plat_collective  
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Lyrics:

Is this x defined?
Is f continuous?
How do you find out?
You can use the limit process.

Approach from both sides,
The left and the right and meet.
Im a just a limit, defined analytically

Functions continuous,
Theres no holes,
No sharp points,
Or asymptotes.

Any way this graph goes
It is differentiable for me for me.

All year, in Calculus
Weve learned so many things
About which we are going to sing

We can find derivatives
And integrals
And the area enclosed between two curves.

Y prime oooh
Is the derivative of y
Y equals x to the n, dy/dx
Equals n times x
To the n-1.

Other applications
Of derivatives apply
If y is divided or multiplied
You use the quotient
And product rules

And dont you forget
To do the dance

Also oooh (dont forget the chain rule)
Before you are done,
You gotta remember to multiply by the chain

(Instrumental solo)

I need to find the area under a curve
Integrate! Integrate! You can use the integration

Raise exponent by one multiply the reciprocal
Plus a constant
Plus a constant
Add a constant
Add a constant
Add a constant labeled C
(Labeled C-ee-ee-ee-ee)

Im just a constant
Nobody loves me.
Hes just a constant
Might as well just call it C
Never forget to add the constant C

Can you find the area between f and g
In-te-grate f and then integrate g
(then subtract)
To revolve around the y-axis
(integrate)
outer radius squared minus inner radius squared
(multiplied)
multiplied by pi
(multiply)

Multiply the integral by pi!

Pi tastes real good with whipped cream!

Mama-Mia, Mama-Mia
Mama-Mia let me go.
Pre-calculus did not help me to prepare for Calculus, for Calculus, help me!

So you think you can find out the limit of y?
So you think youll find zero and have it defined
Oh baby cant define that point baby
Its undefined
Goes to positive and negative infinity

Oooh. Oooh yeah, oooh yeah.
Differentiation
Anyone can see
Any mere equation
It is differentiable for me.

(Any way this graph goes)