lirik lagu math yo! – the calculus rap/ yo math!
[part 1: the calculus rap]
[simon]
let r be the region enclosed by the graph of f of x equals x to the 4 minus 2.3 x to the third 3 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 it’s no debate
the volume is 98.868
[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)
[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!
[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
take it again to find its concavity
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