Calculus Rhapsody (explained)

Beberapa hari yang lalu, saya nemu video di Youtube yang berjudul “Calculus Rhapsody”. Isinya adalah lagu Bohemian Rhapsody (by Queen) yang liriknya diplesetin jadi tentang kalkulus gitu deh. Emang sangat agak maksa sebenarnya liriknya, tapi cukup kreatif sih. Isinya juga cukup berguna buat belajar kalkulus beneran, hehehe.. Tapi orang2nya kok kayak pada hiperaktif gitu ya, hahaha.. Ok, langsung aja check this out:

berikut liriknya beserta penjelasan (bagi yang gak paham kalkulus maaf2 saja yaa :-P) :

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' 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

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

Im 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 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.. can't define that point baby
It's 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)

PENJELASAN:

Dalam lagu ini terdapat sifat-sifat dalam kalkulus yang terkandung, di antaranya:

  1. Apakah x terdefinisi? apakah x kontinu? Gunakan proses limit buat mengetahuinya. Dekati dari kiri dan kanan, jika nilainya sama maka mempunyai limit di x. Jika nilainya sama dengan f(x), maka fungsi kontinu.
  2. Fungsi kontinu tidak memiliki lubang, titik tajam, sama asimtot.
  3. y’ berarti turunan dari y, jika y=x^n, maka y’=dy/dx=nx^(n-1)
  4. Terdapat beberapa aplikasi dalam turunan, antara lain aturan perkalian dan pembagian, serta aturan rantai. Juga jangan lupa untuk menari??U
  5. Untuk mencari luas di bawah kurva, gunakan integral. Integral dari x^n adalah 1/(n+1) * x^(n+1) +C (–> jangan lupa, ditambah konstanta)
  6. Untuk mencari luas yang dibatasi f(x) dan g(x), integralkan keduanya, lalu cari selisihnya.
  7. Untuk mencari volume benda putar, jari-jari luar di kuadratkan, dikurangi jari-jari dalam dikuadratkan, lalu dikalikan pi.
Yapz, sekian penjelasan yang terkandung dalam lagu Calculus Rhapsody yang sebenarnya tetap tidak membantu dalam ujian kalkulus.. Selamat menikmati videonya, hehehe..
CMIIW
Advertisements

2 comments on “Calculus Rhapsody (explained)

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s