The Calculus Rap/ Yo Math!

[PART 1: The Calculus Rap]

[Verse 1: Simon]

Let R be the region enclosed by the graph of F of X equals X to the 4 minus 2.3 X cubed plus 4

And the horizontal line Y equals 4 as shown in the figure above

Find the volume of the solid when R is rotated about the horizontal line Y equals -2

Looking at the problem, what's the criteria

Volume's the anti-derivative of area

Got a rotation so it's washer method time, so

Take that integral multiply by pi

Find each distance to the axis

Squaring 'em and subtracting 'em is our tactic

Hit math 9 there's no debate

The volume 98.868

[Verse 2: Liam]

L'Hopital

Optimal

Get me to a hospital

Find the limit of the fraction

0. 0. Now there's action

YUH (WHAT?!) x6

Derive the top and the bottom

Solve for X

You know we got 'em (YUH)

[Verse 3: Ryan]

Ay yo here we go

Calc rap 2 baby!

Behind the walls of tangent slope. life is defined

I'm thinking calculus when I'm in the AP state of mind

7 in the morning looking at graphs and f and f prime

Please don't change the slide, I still need some more time

Processing, also known as my middle name

F prime of x equals the limit as h approaches 0 of f of x plus h minus f of x over h

Engraved in my main frame

This can only be true provided the limit exists

Just like how because I'm a calc god I got ice on my wrists

Differentiability implies local linearity

Instantaneous rate of wait- are you paging into surgery

Deriving and thriving, multiplying, vibin' and maximizing my thinking cap 'cause this is the calculus rap!

[Verse 4: Luciano]

Hold up, let me take a step back and look at this

Ohhhh, fundamental theorem of calculus

Alright, I got this

2 parts, split like an atom

But first we got to find the right function to throw at 'em

It's gotta be continuous

Now for the part where we actually do calculus

Set g as an integral make it a derivative now things are getting critical

Define the area under a curve

Do the anti differentiation that we all deserve

Got that?

Any Questions?

No? Alright next part

Second part

We gotta get the bound

Doing calculus while we're sitting on these mounds

Pretty simple really

Just plug it in. And know that you got the area for the win

Now go on, integrate and thrive

Listen to the calc rap, and you'll get a 5

[PART 2: Yo Math!]

{Will and Sergio}

When you've got no calculator

How are you supposed to find the integral?

Well there's this thing called Riemann approximations

It's not complicated I'll show you how

When you took my calculator

I had thought I'd see you later

But now you're gone and I don't know how

I'm supposed to find this integral?

Midpoint, trapezoid, right, and left

Riemann sums got me feelin' bereft

Cause it's a hassle workin' with rectangles

And equal subdivisons are a whole 'nother deal

Even, odd, or neither, all I feel is pain

Cause the area of the approximation will never be the same

Fundamental theorem of calculus

Is gettin' real difficult because you left

Fundamental theorem of calculus

Implications of the anti derivative

Love differential from A to B

Continuous as well as its time to find point C

Taking the derivative to find its maximum