Best of luck on the final, my summer calc 2 students! Check out this integral by Mu Prime math! kzread.info/dash/bejne/houWzNOCc5S6lKQ.html

We have so much technology, so many tricks to learn, so many ways to represent things, but a man in front of a whiteboard still manages to be the best resource for really learning and engaging with the math that students recognize as important. Thank you for your work, I hope teachers everywhere are inspired.

@blackpenredpen

5 жыл бұрын

Aww thank you Matthew! I am very happy to hear this!!

@That_One_Guy...

Жыл бұрын

You still use technology anyway the moment you watch this video on KZread, i wouldn't ever know about bprp at all if it wasn't for this site, instead i would still stupidly rote memorizing math formula.

What they teach you in class: integrate 2x What they put on the test: derive the arc length of a parametric equation formula

When you have no idea what is going on but you watch it anyway...

There is an easy "intuitive" way to remember this that you might want to show (it makes the formula derivable in a second). Resolve an infinitesimal length of curve into its components in the radial direction and the theta direction. The first one has length dr, and the second has length r*d(theta) (arc length formula). Hence dL = sqrt(dr^2 + r^2 d(theta)^2) ----> your result

This was exactly what we needed. Thank you!

Best of luck on the final we all with u

Loving these proofs! Thanks!

2:40 What's the product rule? I have always used the Prada Lu instead :)

@LS-Moto

5 жыл бұрын

You use the product rule, you live by the prada lu

@blackpenredpen

5 жыл бұрын

I meant to use the Prada Lu!

@neilgerace355

5 жыл бұрын

@@LS-Moto thank you Lars, I hope you are well

@alexdemoura9972

5 жыл бұрын

This "polar" thing reminds me a hack I was used to do in Casio graphic calculators. I know there are many Casio calculators fans here in blackpenredpen, just as I was, and I believe I still am. Bprp himself already presented some math techniques on a Casio fx for those who need a companion calculator on their exams. For those who want to investigate iterative functions described as: xₙ₊₁ = f(xₙ) It takes advantage from the rectangular coordinate variables have the same position in memory of polar coordinates variables: X same as r, and Y same as θ. And graphing functions do not affect these X and Y variables. The two conversion functions in Casio calculators related to Rectangular and Polar coordinates are: X, Y

Thank you, my book (like most) just glosses over everything and gives the final formula which does students a disservice.

Thank you so much! Love your simple explanations! I just realized how calculus is beautiful but our uni proffesors failed to show us that

I really need proofs for formulas so thank you!

Thank you man That was really helpful

Great proof! Good luck to those who will have final!

1:24 "here is the dL" lol

@blackpenredpen

5 жыл бұрын

Mu Prime Math hahaha I just noticed that too

I’m so glad that I was able to follow a blackpenredpen video

Videos like this deserve more likes

Really helpful for my prmo exam :)

Hey Blackpenredpen. Can you do a series on doinh engineerinh problems with integral or differential equations? thanks.

TYSM SM SM SM SM

Very nice!

All I was waiting for - Wouldn't it be nice ....

Oooohh proof I love proof!

Actually I liked your video too much /(love from India 🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳)

@blackpenredpen

5 жыл бұрын

Red Ron Tech thank you!!

god. damn. boi you killed that sh*t

Can you make a video of the geodesic of a polar curve? (In 3D if possible)

Good! I hope you have also already understood the domain of r is [0,infinity].

Using Lagrange’s Version of Taylor’s Theorem; you can prove that the absolute value of the sum from k=n to infinity of x^k/k! Is less than or equal to exp|x| * |x|^n/n! Do a video on this

Great!

Cool!

Your smile is pretty.

It is Blackpenredpen that did so that I could differentiate and integrate almost everything, as an 13 year old. Thank you!

@henryginn7490

5 жыл бұрын

HaZeX integrate e^x^2

@elie.makdissi

2 жыл бұрын

@@henryginn7490 that's an overkill

That is cute. :)

What if the limits are the same, ie i'm integrating over a loop. the arc length is certainly not 0, but equal limits means integral is 0?

@turtlellamacow

5 жыл бұрын

The limits shouldn't ever be the same, even if the curve loops back on itself. For example, if it's a simple circle, r=3 for example, the limits are 0 to 2pi because a full revolution is an angle of 2pi. (You must be careful and always consider what range of angles corresponds to one full loop around the curve because, maybe unexpectedly, it's not always 2pi!)

@vivi-fe5rj

3 жыл бұрын

I know that this is a year old comment, but for anyone wondering in the future, equal limits (2pi and 0, say in a cartioid) do sometimes result in zero. To avoid this, try and use symmetry when possible. For example, the arc length of a cartioid of equation r=1-sin(theta) can be integrated by using the property of symmetry about the theta = pi/2 axis. Thus, you can integrate from -pi/2 to pi/2, multiplying the final answer by 2, and you will get a real number.

I |love| everytime he says squaaare root

2:00 Could not understand this step. Thanks for the result.

@stephenbeck7222

5 жыл бұрын

He’s using the formula for arc length of parametric functions. You’ll want to look that up.

thanks

Yay!!!!

@mathemagicallearning9593

5 жыл бұрын

Oon Han Hi!!

@OonHan

5 жыл бұрын

@@mathemagicallearning9593 Hey!!

@blackpenredpen

5 жыл бұрын

Hey!!

Here is the deeel...❤❤

Can you do a video explaining the meaning of the integral sign

@not_vinkami

5 жыл бұрын

It is just a stretched S

@egeyaman4074

5 жыл бұрын

S of sum

@Ken-no5ip

2 жыл бұрын

Integrals can be represented as infinite sums

@d-hat-vr2002

11 ай бұрын

S for summa (sum). It's the traditional long-s lowercase letter form. Before about 1800, the familiar 's' lowercase letter was only used at the ends of words and the long-s character was used everywhere else.

I didn't understand why you added the d(theta) at rhe end of the first formula. Just the square root should be the differential length

@d-hat-vr2002

11 ай бұрын

Here's how I sort of understand it: dL = sqrt(dx^2 + dy^2) is the length formula in the notation of differentials and intuitively he's trying to integrate both sides of this equation. But we need a dθ in there because we're really integrating over a θ range. So we multiply the right side by 1 in the form of dθ / sqrt(dθ^2), assuming dθ > 0. This proof seems informal: he treats the left side as an indefinite integral over L (which would have limits of integration L1 to L2, not sure what that means) but the right side as a definite integral over θ. Textbooks usually present this proof more precisely, using a Riemann sum definition.

Am i the only one who didnt understand shite but liked the video anyway

You used the green pen and the blue pen.😂

The heck happened at 1:14??

@neilgerace355

5 жыл бұрын

I think he elected not to edit out this bit, that's all :)

s'il vous plait integral x/(exp(x)-1

@benjaminbrady2385

5 жыл бұрын

Well, that's just the bose integral of two. Which is (2-1)! * Zeta(2) which is equal to (pi^2)/6 A video would be pretty nice though too :)

Black pen rainbow pen

whoops, forget to edit. Try this integral: $(2x^7 + 5x^6 + 13x^5 + 20x^4 + 21x^3 + 16x^2 + 7x +4)/[(x^2 + x +1)^2 (x^2 + 2x + 2)(x-1)^2]dx PFD constants are integers. From Spivak :)

@typo691

5 жыл бұрын

uhhhhhhh

@aeb4865

5 жыл бұрын

Ok it doesn’t *seem* hard it just seems like it is gonna be frustrating

blackpenredpen...bluepengreenpen?

Sir can you pls tell me the solution of an intergral where limits are from -pi to pi and equation is [cos^2(dx)\1+a^x]dx

Polar? Para.

Hi

@blackpenredpen

5 жыл бұрын

hi

@NoNameAtAll2

5 жыл бұрын

Hi

Are you feeling ok bprp? To me, you are a sounding a bit flat in this video. I hope nothing is wrong.

@blackpenredpen

5 жыл бұрын

Neil Gerace Oh this was actually filmed a few months ago. I think I did this after teaching my class. So I was tired. Thank you for asking! : )

I thought it just integral r dtheta

Now we know: (dx)²+(dy)²=(r dθ)²+(dr)²

the dL = the downlow.... lul

@blackpenredpen

5 жыл бұрын

I thought you said download.... but I looked that up....

Calculus BC

4:33 INVALID!! I'm mathematically scorned by this invalid notation.