Calculus Rhapsody
new lyrics by Mike Gospel and Phil Kirk
may be sung to the tune of "Bohemian Rhapsody"
by Queen
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.
I'm just a limit,
defined analytically
Function's continuous,
There's no holes,
No sharp points,
Or asymptotes.
Anyway this graph goes
It is differentiable for me ...
for me.
All year, in Calculus
We've learned so many things
About which we're going to sing.
We can find derivatives
And Integrals
And the area enclosed between two curves.
y' ... 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 don't you forget to do the dance ...
Also ... oooh
(don't forget the chain rule).
Before you are done,
You gotta remember
to multiply by the chain.
I need to find the area under a curve
Integrate! Integrate!
You can use the integration.
Raise the exponent by one
Multiply the reciprocal.
Add a constant. Add a constant.
Add a constant. Add a constant.
Add a constant labeled C.
Labeled C.
I'm just a constant, nobody loves me.
He's 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?
Integrate f and then integrate g.
Then subtract.
To revolve around the y-axis
Integrate outer radius
minus inner radius squared.
(multplied) 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!
Precalculus did not help me prepare for
Calculus, for Calculus, help me!
So you think you can find out the limit of y?
So you think you'll find zero and have it defined?
Oh baby ... can't define that point baby.
It's undefined ...
Goes to positive and negative infinity.