The p-integral Proof (type 1 improper integral)

[@VechtMalthos]

I showed this to my cat. He looked at me funny and walked off.

[@blackpenredpen]

Vecht Oh mannn!!

[@g00zik97]

cade

[@emperorpingusmathchannel5365]

He doesnt like it when Steve uses the blue pen

[@itsiwhatitsi]

Lol

[@ianmoseley9910]

Should have pawsed it for him

[@98danielray]

just wanna take the time to thank the great educational job you do here

[@blackpenredpen]

Fractal thank you!!!!

[@blackpenredpen]

Hi~

[@letsgetiton99]

Hi

[@letsgetiton99]

wanna ask how to integrate indefinitely of 1 over cos (2x) minus cot (2x) . im a beginner

[@steve2817]

Hi!

[@aurithrabarua4698]

Hello!!!!!

[@yaleng4597]

Say.Is it Peyam?

[@xevira]

The hood went up.. you know things are about to get real.. or complex... or non-elementary... you never really know with calculus.

[@wnjstudio4907]

maybe things are getting series

[@roderickwhitehead]

No joke, my cat just watched this video with me.

[@blackpenredpen]

R.C. Whitehead nice!!!!!

[@pinklady7184]

Your cat loves BlackPenRedPen himself.

[@drpeyam]

Haha, that’s what I call the Peyam test in class 😄

[@blackpenredpen]

Dr. Peyam's Show nice!

[@JoshuaHillerup]

I like doing pintegrals

[@ffggddss]

So, you have a pinterest in them? Fred

[@srpenguinbr]

left a like and put in my Watch later playlist

[@blackpenredpen]

Felipe Lorenzzon :)))))

[@abrarshaikh2254]

You can also prove that using P-series (zeta function) As series is convergence for p>1 only , hence integral will be also convergence for same

[@thefallinglink]

I expected it to converge for p>1 because this problem looks so similar to the p-series convergence test, but as an integral rather than a series. I'm guessing the connection is how integrals can be defined by Riemann sums with infinite rectangles, which is an infinite series?

[@CharlesPanigeo]

You are correct. Look up the integral test for convergence.

[@98danielray]

pretty much

[@TheNachoesuncapo]

You are such a good teacher!are you still running marathons?

[@blackpenredpen]

Nacho I am. March 24th, LA marathon!

[@TheNachoesuncapo]

@@blackpenredpen YAY!!great to hear

[@mike4ty4]

@@blackpenredpen Why do you do that _AND_ the maths stuff instead of just one XOR the other? Is it NECESSARY to do both instead of just one XOR the other? Are you a BAD person if you only do one, but not the other?

[@tempestandacomputer6951]

@@mike4ty4 what?

[@likris6607]

This is lifesaving ! I know my cal II test tmr will have at least one question related to this !!!

[@nolann2382]

he explains this way better than my teacher did I finally somewhat have an understanding of this

[@rockyk6805]

This is a really good video man! Nice work!!

[@wouterdeniz]

Know thy integrations and believe thy limits - Chain Lu (2019)

[@beril7568]

Sir you are like a lifesaver calculus angel. Thank u very much😊

[@viridianatirado5374]

my go to youtube channel to pass this calc 2 course!

[@JoseShajiOfficial]

thank you so much!

[@hauler-hx6gw]

Here's a problem given to me in a math competition I had today that literally no one figured out in time Let lzl=5 and Im {z}>0. If the distance between (1+2i)z^2017 and z^2019 is maximized, then determine Re{z^4} + Im{z^4} Reply for correct answer if needed

[@Babidi123]

Is answer -875?

[@Rsharlan3]

I get 125.

[@mrmartin988]

Pretty sure z=5exp(I*pi/3), sound right?

[@goitomgebremeskel-c9o]

i appreciate this expression because you made it simple though it seems difficult!!!!!!!!!!!

[@krukowstudios3686]

More of these videos where you end up with a formula! :D

[@pachu72lee57]

Thank you so much, I was wondering what my professor was doing but now I get it.

[@leesin1077]

This reminds me a bit of the geometric series or atleast some sort of special case of it. Is there a connection?

[@oaitseslave5402]

Lets give this guy his flowers !

[@chillproductive]

Amazing explanation!

[@AronGirmay-l9l]

continue bro you are great

[@emilygrootkarzijn6944]

thanks for making late night maths fun :)

[@MyNordlys]

On the same way, serie from 1 to infinite of 1/n diverges and serie from 1 to infinite of 1/n² converges.

[@imanolmanzanares5000]

always believe in the math!! nice video broo

[@habibhassan4015]

Just did this problem in class on Friday.

[@blackpenredpen]

Habib Hassan nice!!

[@PaGow]

I saw this video last year, before I was doing calculus and I would never guess that I would need it today😅 Man...life is funny😂

[@NavyBlueMan]

Here's a question, I just thought of it and don't even know if it's remotely possible to solve, I haven't had time to address it so thought I'd just drop it here: The sum from n=0 to infinity of the INTEGRAL of 0 to n of 1/n! It reuses n 3 times and so I'm not even sure how someone could approach it but still thought it would be worth asking just for fun. Maybe change it from n going to infinity to 1000 or something a bit easier to approach.

[@gabrielag1844]

Once again, you've saved me :)

[@Ironmonk036]

The man is sporting the hoodie on. 🤪

[@videowatcher192]

U are a machine and i like so much your videos

[@blackpenredpen]

Nico Rojas thanks!!!!

[@devananjelito9111]

Excellent!

[@enzoyoussef4440]

Good job bro from Morocco

[@imenelhakim8020]

Thanks a lot !!

[@XXgamemaster]

I still find it very counterintuitive that the p = 1 case diverges. The area under 1/x gets smaller as x goes to infinity so it looks like it should indeed converge. But I guess not...🤔

[@ffggddss]

It diverges, but ve-e-e-ery slowly - logarithmically, in fact. He's apparently going to show in a later video, how this integral ("p-integral") helps analyze the behavior of the p-series ∑₁⁰⁰(1/nᵖ) using what is called "the integral test." When p=1, the series is called the harmonic series, and it too diverges logarithmically. This is counterintuitive for the same reason you gave for the integral. But in fact, there's a famous constant that is defined by having the integral and the series "run alongside each other" all the way to ∞. The Euler-Mascheroni constant is defined by: γ = lim [ ∑₁ᵏ(1/n) - ln(k)] k→∞ Its value is about 0.577... (You may recognize this as the first 3 digits of tan 30º = 1/√3, but, alas, the two don't match after 3 digits.) Fred

[@scarbotheblacksheep9520]

The negative version of the best friend!

[@TotallyOKaYProductions]

thank you

[@saarike]

Very nice!

[@Ivan_1791]

By the way, that integral is equal to 1/(p*ln(p)) for p

[@blackpenredpen]

Álex the Benighted yup : ))))

[@alegian7934]

blackpenredpen, great vid :D also, Im learning about sums and series in university and I need help. Are there any helpful videos on youtube?

[@guguwege1523]

Thankyou

[@johntelegdy105]

What about 1>p> 0 ? Is p an integer?

[@yoonjuliagil]

Thank you for such an amazing video! One question, does the first integral, where p=1, have anything to do with the p-value test (series)?

[@u36reck63]

yes, he is demonstrating in the video how it is known that the p-series converges for p > 1

[@STIVESification]

I guess you could you exponent of convergence to find out for which power it converge which is equals lambda+1

[@aurithrabarua4698]

Is there very cold out there?? 😂😂😂

[@alphonsetyche3278]

p progression 1/x^p p=1 harmonic series

[@asusmctablet9180]

So if p is only infinitesimally greater than one, it converges to one over an infinitesimal, which is still infinity. Ok, got it.

[@SartajKhan-jg3nz]

Isn't this the zeta function?

[@hauler-hx6gw]

Hey, today I went to a math competition and there was this one frq that was really confusing. It had 2 equilateral triangles and a line going through. With those we are supposed to prove two lines intersecting are pi/3 At first it looked simple but then turned out to be seemingly impossible to prove. I later asked about it and it had something to do with the complex plane somehow. Would you be able to figure out what I am talking about and make a video on how to do it

[@19pixels]

Watching this 5 hours before my real analysis exam (I'm not so cooked after all)💀😂

[@markberardi109]

Thanks for another interesting video. While watching the video, it occurred to me I never understood why the integral of 1/x equals ln (x) ?

[@blackpenredpen]

Mark Berardi It's how they defined ln(x) first

[@sebastianmeier5002]

Can you upload a video of the repeated exponential graph? It would be very interesting, greetings

[@connorhall6388]

Shouldnt there be a 3rd case where p=0?

[@sripranav]

Believe in your limits!

[@tryphonunzouave8384]

Why is this an improper integral ?

[@gaminginrealtime1552]

I am taking my first year of math for my bachelor of science. Do you think I should look out for complex numbers at all?

[@98danielray]

youll get it eventually, but if you want it you can

[@98danielray]

at least the intuition for them js important to have

[@gaminginrealtime1552]

@@98danielrayI've dealt with the likes on the square root of negative 1. However, trig like cos(z) = something. Yikes

[@drdonaldduck]

Hi, how can I send you a message? I didn't find any email addresses...

[@Fatih-hy7jj]

What I do not get is that how can that area diverge? It can obviously be seen that it gets smaller and smaller, how come it diverges? I understand all the mathematical operations except for this.

[@Flanlaina]

Type 1 or type 2?

[@ianmoseley9910]

diverges when p = 0?

[@safouaner-ryfy6060]

integrate of cos x/ x

[@safouaner-ryfy6060]

by parts is cosx lnx but cosx/x^4 ?

[@quandaledinglegaming9930]

the drip is continous but not differentiable!

[@HornyKangaroo314]

Can p become negative number? Or is it true for only p>1?

[@XXgamemaster]

Ayip Hikhok The integral diverges for p less than or equal to 1, so that also applies if p is negative.

[@HornyKangaroo314]

@@XXgamemaster ahh thank you.

[@saharhaimyaccov4977]

X^(x-1) ?

[@sebbyteh9203]

Mathematician are triggered seeing him plugging in infinity like a number instead of using limit.

[@ThePharphis]

@5 mins: or just add p to both sides you crazy man!

[@kingphone8824]

I showed it to my dog it run scared heeeeeeeee

[@polaris_babylon]

P-Series

[@alexanderskladovski]

The negative best friend aka the worst friend

[@quantumcity6679]

Awesome video but I think you forgot to switch off AC !!........no? Or Something alse?? 🤔🤒 ....little help needed... How expand (4a+5b+6c+.....8e )===.......if a, b, c be the positive integers ?🤑

[@kingphone8824]

Hi blackpenredpen I am mohammad Daghimen can you make a vedio to how we can Integrate the cube root of(( (x^3_1) ((over x_1 ) ) I love you alot LOL your channel is my favorite on KZbin

[@matthewchuang6707]

I screwed up my math interview in December because of this question.... damn

[@blackpenredpen]

Matthew What interview was it?

[@luisramrod9121]

This is in my calculus book.

[@budtastic1224]

Dr. Chow is in ur calc book?! Amazing!

[@luisramrod9121]

@@budtastic1224 who is chow?

[@budtastic1224]

@@luisramrod9121 bprp

[@somanathgoudar6171]

+blackpenredpen, Hello Sir! Greatly impressed by your content. I have a problem and will be highly obliged if you can address to it. Let f: R--»R be a function which is continuous at 0 such that f(0)=1. Also assume that f satisfies the relation for all x: f(X) - f(X/2) = 3{(X^2)}/4 + X. Find f(3). Thank you. Love from India!

[@yunncchen377]

x--> infinity, lim 1/(x^(p)) -->0, if p>0 or p > 1, how about p=0.01 > 0, the limit will be 0, can you show me the proof?

[@rakhimondal5949]

He's dope

[@서현석-p1l]

Can you make a video that evaluate integral x/(e^x-1)dx x=0 to infinity?? Plz

[@schumensch]

I know that it's not really 5he right video to ask under, but I really don't understand one thing. If you have a definite integral and want to solve it, by using a trig substitution, then you would also have to change the bounds of it, not just the inside. But let's say the integral is from x=-1 to x=1 and you want to bring it to the theta world. With the substitution e.g. x = cos (theta). So you have 1/-1 = cos (theta), then for both 1 and - 1 you have an infinite amount of theta's to choose from. Do you you always have to choose the principal values? How does the choice of one affect the other? Thanks to everyone in advance! PS : I'm a 13 year old from Germany, so if I don't have perfect grammar or spelling or I have a flaw in my logic... Just don't be rude. :)

[@RTD553]

You broke a lot of pure maths rules there mate!

[@A_Sharaawy]

❤❤❤❤❤❤

[@aidambo1522]

matache broo i got it bro

[@fouadsbihi4393]

Do p=i cmlx

[@samuelvernola2609]

I love you

[@AlphaTaurinet]

你太棒了

[@blackpenredpen]

Alpha Tauri thanks

[@youssefbenhachem993]

Hey guys i need help in an integral : integral from 0 to 1 to 1/(1-x) + 1/lnx dx . Thanks

[@bandamkaromi]

hi. all. :-)

[@richardfredlund3802]

my cat just not getting it....perhaps I need to show more times :)

[@andres.robles6]

Hi5

[@rafaellisboa8493]

PLEASE make complex version, formula for 1/(a+bi)^z

[@blackpenredpen]

Ginger Stalin and the limits of integration?

[@98danielray]

the condition is the same

[@98danielray]

converges for Re(z)>1

[@lambdamax]

P-integrals on pinterest

[@physicsphysics1956]

I like your videos, but please use ln(x) instead of ln|x| for the integral of 1/x. Please delete all of your videos and reupload them but without the absolute value.

[@Makabaril]

physics physics why’s that? The second one is correct for a larger domain than the first

[@blackpenredpen]

Jacob Jeffries I did use ( ) in this video. Since I know the interval is pos so no need for abs value.

[@physicsphysics1956]

@@blackpenredpen Still, that is only for this purpose. Please use ln(x) for integrals in general.

[@blackpenredpen]

physics physics How would you integrate 1/x from -3 to -2?

[@physicsphysics1956]

@@blackpenredpen -0.4055

[@noahshomeforstrangeandeduc4431]

Hi

[@ayishashifam9101]

U r very fast...

[@KingV676]

Next time do some exercises okay me bro

[@sei-bay]

Emmy good

[@Ivan_1791]

Too easy.

[@TheNachoesuncapo]

Yeah

[@blackpenredpen]

Yes