A great integral calculus review in one problem!!

Рет қаралды 54,669

3 жыл бұрын

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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Пікірлер: 120

@IoT_ 3 жыл бұрын

Now we need to check the result by differentiation

@noahtaul 3 жыл бұрын

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

@red0guy 3 жыл бұрын

yeah

@megauser8512 3 жыл бұрын

Yes, he forgot that.

@Aditya-jv9mp 3 жыл бұрын

Yeah left me confused a little bit

@duckymomo7935 3 жыл бұрын

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

@WielkiKaleson 3 жыл бұрын

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

@robshaw2639 3 жыл бұрын

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 Жыл бұрын

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!

@tylerm442 3 жыл бұрын

All it's missing is integration by parts lol

@beoptimistic5853 3 жыл бұрын

kzfaq.info/get/bejne/jrd5ldFjnMqzmnk.html 💐👍

@vittorio1159 3 жыл бұрын

Now check the answer by differentiation ...by definition

@anshumanagrawal346 2 жыл бұрын

Lol

@JCCyC Жыл бұрын

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

@hsjkdsgd 3 жыл бұрын

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!

@johnnath4137 3 жыл бұрын

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.

@lucashoffses9019 3 жыл бұрын

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

@bakul1978 3 жыл бұрын

Yes

@dujas2 3 жыл бұрын

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.

@mcbeaulieu Жыл бұрын

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

@Verifyourage Жыл бұрын

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

@JvnKnght Жыл бұрын

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

@diniaadil6154 2 жыл бұрын

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.

@muskyoxes 3 жыл бұрын

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

@schrodingerbracat2927 2 жыл бұрын

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.

@frozenmoon998 3 жыл бұрын

Hardest integral on KZfaq: Prof. Penn: *Hold my beer*

@Fun_maths 3 жыл бұрын

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

@rafael7696 3 жыл бұрын

Great video, as always

@goodplacetostop2973 3 жыл бұрын

19:22 Loading 94.9%...

@integralboi2900 3 жыл бұрын

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

@berzerksharma 3 жыл бұрын

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

@megauser8512 3 жыл бұрын

Yes, he did!

@andrewdsotomayor 3 жыл бұрын

Yeah, I noticed that as well

@SlidellRobotics 3 жыл бұрын

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

@bakul1978 3 жыл бұрын

@@SlidellRobotics Yes

@holyshit922 Жыл бұрын

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

@roberttelarket4934 3 жыл бұрын

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

@Pauldyke 3 жыл бұрын

Finally, some fun stuff!!!

@TheOneThreeSeven 3 жыл бұрын

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

@DeanCalhoun 3 жыл бұрын

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!

@FoxtwoPC 2 жыл бұрын

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

@The1RandomFool 3 жыл бұрын

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 2 жыл бұрын

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

@sophieward7225 3 жыл бұрын

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

@matematicaconjuliocesar6366 3 жыл бұрын

Excelente

@antarctican5284 3 жыл бұрын

I started by u subbing the whole thing

@FatihKarakurt 3 жыл бұрын

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 жыл бұрын

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

@yousifkhalil9655 3 жыл бұрын

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 жыл бұрын

really good

@get2113 3 жыл бұрын

His integration tricks are great

@michaelfisher9053 3 жыл бұрын

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.

@jack-jt2lm 3 жыл бұрын

very nice teacher

@musatebi486 3 жыл бұрын

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

@megauser8512 3 жыл бұрын

LOL!

@omachiyogi 3 жыл бұрын

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

@CTJ2619 2 жыл бұрын

i lik it when you explin PFDs

@AmrishKelkar 2 жыл бұрын

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

@Chalisque 3 жыл бұрын

KZfaq 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'.

@sankimalu 3 жыл бұрын

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

@EyadAmmari Жыл бұрын

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

@user-A168 3 жыл бұрын

Good

@jimcameron6803 2 жыл бұрын

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

@samegawa_sharkskin 3 жыл бұрын

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

@ArgumentumAdHominem 3 жыл бұрын

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

@ameerunbegum7525 3 жыл бұрын

*NOICE*

@qillerdaemon9331 3 жыл бұрын

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 жыл бұрын

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

@qillerdaemon9331 3 жыл бұрын

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

@CM63_France 3 жыл бұрын

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",

@mbarkaitkerrou6734 3 жыл бұрын

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

@Paul_Hanson 3 жыл бұрын

non

@jamirimaj6880 3 жыл бұрын

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

@josephcollar5987 3 жыл бұрын

What's the damn point....🙄😒

@RobertMOdell 3 жыл бұрын

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

@dougjohnson4917 3 жыл бұрын

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

@lexinwonderland5741 Жыл бұрын

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

@user-lr8od4uz1n 3 жыл бұрын

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

@davcaslop 3 жыл бұрын

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

@atrakchi2 3 жыл бұрын

vielen Dank es war Großartig Danke nochmal

@sushantyadav7806 3 жыл бұрын

Where does this arc word came..not understood

@vaxjoaberg9452 3 жыл бұрын

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

@Daniel-ef6gg 3 жыл бұрын

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

@anilsharma-ev2my 3 жыл бұрын

Taking square root of integration gives us what ?

@123ucr 3 жыл бұрын

This would be a Calculus 2 final problem.

@jaimeenriquediazdiaz2341 2 жыл бұрын

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

@nontth5355 2 жыл бұрын

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

@leif1075 2 жыл бұрын

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

@klementhajrullaj1222 2 жыл бұрын

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

@user-jc2lz6jb2e 3 жыл бұрын

Is Michael Penn short for Michael Pennsylvania?

@Scaw 3 жыл бұрын

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

@johnnath4137 3 жыл бұрын

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 жыл бұрын

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

@mza3764 3 жыл бұрын

someone is playing fp shooter in the background

@juanmolinas 3 жыл бұрын

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

@AstroB7 3 жыл бұрын

Wrong answer Mike

@jabunapg1387 3 жыл бұрын

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

@Ni999 3 жыл бұрын

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.

@jackthisout9480 2 жыл бұрын

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

@Tiqerboy 3 жыл бұрын

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.

@neilg2256 3 жыл бұрын

太复杂了，草稿纸要写三张

@robshaw2639 3 жыл бұрын

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

@duckymomo7935 3 жыл бұрын

Integral Sqrt(tanx) is a nightmare

@Ni999 3 жыл бұрын

Not this way - _Integral of sqrt(tan(x)) ... Impressive method...calculus concepts_ kzfaq.info/get/bejne/mrpolZuoptC4e4E.html Minor typo in it, I mentioned in the comments.