A great integral calculus review in one problem!!

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We look at a nice integral that serves as a review for much of a second semester calculus course.
Playlist: • Interesting Integrals
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Опубликовано:

25 ноя 2020

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Комментарии : 120

@IoT_ 3 года назад

Now we need to check the result by differentiation

@noahtaul 3 года назад

10:55 You need an extra 1/2 on the front of these next two integrals because you removed the parentheses

@red0guy 3 года назад

yeah

@megauser8512 3 года назад

Yes, he forgot that.

@Aditya-jv9mp 3 года назад

Yeah left me confused a little bit

@duckymomo7935 3 года назад

So it should be 1/4 and 3/4 in front of later integrals

@WielkiKaleson 3 года назад

Very true, but... Would that make the final result less nasty?

@tylerm442 3 года назад

All it's missing is integration by parts lol

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐👍

@robshaw2639 3 года назад

I just realized that not only is Micheal Penn an extraordinary instructor, but he has great Mathematical agility over a diverse set of subfields... i predict Micheal will discover why the Monster group is what it is, or will make some completely new groundbreaking contribution to Mathematics in his lifetime. I just hope that i live to see it....

@lexinwonderland5741 Год назад

the guy studies VOAs and other things that modern physics is still looking for, I wouldn't be surprised if he or more likely one of his students made a fantastic discovery about that sort of thing. but me too, i'll be thrilled to watch his career!

@vittorio1159 3 года назад

Now check the answer by differentiation ...by definition

@anshumanagrawal346 2 года назад

Lol

@JCCyC Год назад

(Insert meme of Mojo Jojo and Him shedding tears of joy)

@lucashoffses9019 3 года назад

Oh my god He never noticed that he forgot to distribute 1/2 to the second integral.

@bakul1978 3 года назад

Yes

@johnnath4137 3 года назад

More simply: 1 = A(1 - u + u²) + (Bu + C)(1 + u): setting u = -1 → 1 = 3A → A = 1/3; setting u = 0 → 1 = 1/3 + C → C = 2/3; equating coefficients of u² → 0 = 1/3 + B → B = -1/3.

@hsjkdsgd 3 года назад

He carried all the 3 integrals to the very end when he could've easily annihilated the two of them (1/1+u & 1/t) just after partial fraction decomposition. Great display of patience!

@dujas2 3 года назад

That substitution seems like it comes out of left field, but it can be done in 3 steps. First, x=arctan t to remove the trig, t=v^3 to get rid of the cube root and set up partial fractions, then finally u=v^2 to simplify.

@diniaadil6154 2 года назад

u = tanx^(1/3) does help getting to a rational function but with u^6 in the denominator which can be simplified further with a u² substitution. Overall it's the same as using your method but it's much more intuitive to simplify step by step rather than comming up with an overly complicated substitution.

@goodplacetostop2973 3 года назад

19:22 Loading 94.9%...

@integralboi2900 3 года назад

I just realized the loading percent is Michael’s subscribers…

@berzerksharma 3 года назад

I guess u missed a 1/2 while decomposing the integrals

@megauser8512 3 года назад

Yes, he did!

@andrewdsotomayor 3 года назад

Yeah, I noticed that as well

@SlidellRobotics 3 года назад

Yes. At 11:44 he needs parentheses around all but the leading 1/2.

@bakul1978 3 года назад

@@SlidellRobotics Yes

@muskyoxes 3 года назад

The lesson i got out of this is that it's somehow possible to do a ton of work on an integral without ever using integration by parts

@frozenmoon998 3 года назад

Hardest integral on RU-vid: Prof. Penn: *Hold my beer*

@Fun_maths 3 года назад

Hold my chalk, wait don't hold it I need it to write on the board

@schrodingerbracat2927 2 года назад

for partial fraction decomposition, here is a trick I discovered:- by the "cover-up rule", you can get 1 / 3(u+1) easily. then you COMPUTE 1 / (u+1)(u²-u+1) - 1 / 3(u+1) ALGEBRAICALLY to get (2-U) / 3(u²-u+1). So there is no need to solve for A, B, C.

@TheOneThreeSeven 3 года назад

12:32 dt ear muffs !!!!! can we get that in the merch store please =)

@mcbeaulieu Год назад

Even your "2u" has music to it. That's perfection right there 🙏

@Verifyourage Год назад

At 11:00 multiply the numerator by (2) = 2u-4 then multiply by 1/2 outside the integral to get 1/4 apply the sum rule 2u-1/ u^2-u+1 minus 3/u^2-u+1

@rafael7696 3 года назад

Great video, as always

@FoxtwoPC 2 года назад

I always always forgot to add a constant to indefinite integrals...my exam answers were always pages of triple checked algebra that resulted in -2pts for forgetting the +C

@JvnKnght Год назад

"That's kind of a bummer" at the end when subbing back for x. Had me laughing my ass off

@roberttelarket4934 3 года назад

Michael Penn the "energizing bunny" cranking one great math video after another!

@Pauldyke 3 года назад

Finally, some fun stuff!!!

@DeanCalhoun 3 года назад

I think watching your videos is working because I was able to intuitively guess pretty much every step along the way. What a great integral. Thank you so much for your videos!

@holyshit922 Год назад

If we play with substitutions we can get following u=sqrt(3)(1-(tan(x))^(2/3))/(1+(tan(x))^(2/3))

@FatihKarakurt 3 года назад

combine the first two ln functions to get back the (1+u^3) in the argument which will simplify the result a bit.

@FatihKarakurt 3 года назад

@@angelmendez-rivera351 Yeah, it seems I made a sign mistake as well.

@sophieward7225 3 года назад

I like ya cut, P! *slaps down integral of 1/cbrt(tanx)*

@musatebi486 3 года назад

I cant focus on the problem, I want to press play button on his shirt but it does not work.

@megauser8512 3 года назад

LOL!

@The1RandomFool 3 года назад

As an alternative, you can do a substitution u^3 = cot x. After simplification, you can substitute again with u^2 = v the rest is similar to the video.

@leif1075 Год назад

Whybwoukd anyone pick the isub he did right..isn't it random out of nowhere

@omachiyogi 3 года назад

3:47 I usually just use the positive square root too. However, why can we just do this instead of considering +-sqrt(u)?

@antarctican5284 3 года назад

I started by u subbing the whole thing

@matematicaconjuliocesar6366 3 года назад

Excelente

@get2113 3 года назад

His integration tricks are great

@AmrishKelkar 2 года назад

Try the integral of the reciprocal of the fifth root of tan x!!

@yousifkhalil9655 3 года назад

only u sub, trig identities, simplification, partial fractions, cubic factorization, completing square, add & subtract a quantity, dismantle integral and t sub in a u sub! i thought there were gonna be a trig sub, by parts, long division, multiply by conjugate, multiply numerator and denominator by another function (as with secx) and a use of definite integration properties with infinite intervals and discontinuous integrands as well

@avalanche2022 3 года назад

really good

@jack-jt2lm 3 года назад

very nice teacher

@Chalisque 3 года назад

RU-vid displays suggested videos and your channel logo at the end (20s from the end of the video), which obscure the blackboard. Perhaps when you edit you can squeeze an extra 20s at the end after your 'good place to stop'.

@CTJ2619 2 года назад

i lik it when you explin PFDs

@michaelfisher9053 3 года назад

The constant multiplying the arctan term should be 1/2 sqrt(3). The constant multiplying the ln(tan tan) term should be -1/4. Otherwise he nailed it.

@RobertMOdell 3 года назад

shouldn't the natural logs at the end be surrounded by absolute value ?

@sankimalu 3 года назад

I like the multitasking: integrating household chores with educating the masses.

@lexinwonderland5741 Год назад

Is there any way to reduce functions of the form arctan(k*tan(x))?

@user-A168 3 года назад

Good

@dougjohnson4917 3 года назад

Why not make it an arc tan function at 4:24?

@qillerdaemon9331 3 года назад

Great! Wonderful! Except it's the final, there are 10 problems almost identical to this one, I have an hour to complete the exam. And I've just spent almost 20 minutes solving one of them. :(

@abraarmasud9194 3 года назад

If this is an informal exam, maybe we can help you out. Share the question?

@qillerdaemon9331 3 года назад

@@abraarmasud9194 It was just a joke, buddy. :)

@mbarkaitkerrou6734 3 года назад

Monsieur Michael Penne est est-ce que vous pouvez trouver cette primitive sans utiliser le changement de variable et mercis infiniment.

@Paul_Hanson 3 года назад

non

@CM63_France 3 года назад

Hi, Got the missing 1/2 as well, or the missing parenthesis. Why Penn whith 2 n's? For better SEO ? :D For fun: 3 "ok, great", including 1 "ok, great, so now let's go ahead and", 1 "I'll go ahead and", 1 "but let's go ahead and",

@ameerunbegum7525 3 года назад

*NOICE*

@EyadAmmari Год назад

Just a note that you forgot to carry a 1/2 when you were breaking up the quadratic part.

@user-lr8od4uz1n 3 года назад

15:23 I never expected that M'kay really exists

@jamirimaj6880 3 года назад

Folks, remember: This is the EASY way of doing this. 😑

@josephcollar5987 3 года назад

What's the damn point....🙄😒

@samegawa_sharkskin 3 года назад

i thought this would be like bprp's integral video of cbrt(tan(x)) and got scared but it's really not as bad as that

@davcaslop 3 года назад

17:25 why didn't he use absolute value?

@jimcameron6803 2 года назад

I was going to watch this, but I went and watched blackpenredpen's video on the same integral instead. It was a classic RU-vid-substitution.

@user-jc2lz6jb2e 3 года назад

Is Michael Penn short for Michael Pennsylvania?

@Scaw 3 года назад

That suggests that Billy Connecticut fought Joe Louisiana twice for the heavyweight boxing championship of the world in the 1940's.

@johnnath4137 3 года назад

I looked him up in Wikipedia and was puzzled about the strange stories I was reading about his politicking and other shenanigans, and nothing about his maths. At long last I realised that I was reading about one Michael Pence (who is he anyway?) whereas I should have been looking up Michael Penn.

@duckymomo7935 3 года назад

He’s from VA www.michael-penn.net/about-me

@atrakchi2 3 года назад

vielen Dank es war Großartig Danke nochmal

@ArgumentumAdHominem 3 года назад

This solution only works if tan(x)>0. What happens when this is not the case

@sushantyadav7806 3 года назад

Where does this arc word came..not understood

@vaxjoaberg9452 3 года назад

Arctangent (arctan) is the inverse of the tangent function. if tan(x) = y, then arctan(y) = x

@anilsharma-ev2my 3 года назад

Taking square root of integration gives us what ?

@Daniel-ef6gg 3 года назад

Looks like you're missing a factor of 1/2 at the 11 min mark

@jaimeenriquediazdiaz2341 2 года назад

Oooh good heair cut, yes perfect and RU-vid lesson mate is ver good so much very much like

@123ucr 3 года назад

This would be a Calculus 2 final problem.

@nontth5355 2 года назад

I just finish my calculus exam and did 1+2=6 and 1-(-1)=3 and lost 2 points. Is there any cure for stupidity? I really need it lol

@mza3764 3 года назад

someone is playing fp shooter in the background

@juanmolinas 3 года назад

wow, what a stunt, I wouldn't have seen it ...

@jabunapg1387 3 года назад

I don't understand what he does there on 11:00 ???

@Ni999 3 года назад

u - 2 ½(2u - 1 - 3) ½(2u - 1) - 3/2 He got ½(2u - 1) + 3/2 from -∫(a-b) = -∫a + ∫b. He still missed multiplying through by the ½ outside of the original parens.

@leif1075 Год назад

WHY ON EARTH would anyone do that substitution of u equals tan^2/3 I don't know why anyone would think of that..

@robshaw2639 3 года назад

After watching this channel for several months now, im really getting a gut feeling that Micheal is the next John Conway...

@klementhajrullaj1222 2 года назад

At the end your hairs! Peace, relax and harmony! ...

@AstroB7 3 года назад

Wrong answer Mike

@duckymomo7935 3 года назад

Integral Sqrt(tanx) is a nightmare

@Ni999 3 года назад

Not this way - _Integral of sqrt(tan(x)) ... Impressive method...calculus concepts_ ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-dT8b8wAjTKM.html Minor typo in it, I mentioned in the comments.

@paulbinu3537 3 года назад

Wrong answer tho

@duckymomo7935 3 года назад

The answer is mostly right except for the constants Sqrt(3)/2 and 1/4 front of log(tan^(4/3)...) which is where he missed the 1/2

@jackthisout9480 2 года назад

A tricky integral he says. I'd say it's pretty triggy.

@neilg2256 3 года назад

太复杂了，草稿纸要写三张

@Tiqerboy 3 года назад

I see your video is 20 minutes, presumably to solve this integral. Wow, can't be easy, especially since I forget most of what I learned way back then. It's not everyday you have to find the antiderivative of trig functions. God, is the answer ever messy! I was watching the MIT Integration Bee. They are only given 4 minutes to solve problems with that.