Trigonometric Integrals - Part 2 of 6

[caligurlnewport]

THANKS!!!!! You explain very well and your website is way better then khanacademy :D

[y0yo21]

why does the 1 and the 1/2 cancel?

[redrum41987]

@y0yo21 he didnt really mean cancel, he meant subtract 0.5 from 1 which is 0.5 which integrates to 0.5x

[VeronicaPinkHeart]

Thanks soo much for this video, I was struggling on a problem like this and found that that it has to be really a tedious problem when integrating even sin and cosine functions!! THANKS SO MUCH!!

[VeronicaPinkHeart]

@marymc14 It's suppose to be a formula. A half- identity formula that you have to use when integrating even trigonometric functions

[paa3617]

Is it necessary to do u-substitution again on (cos4x)/4?

[MissSarahJonnie]

@patrickJMT there's an easier way of solving this. You could just write the square of sin2x divided by 4 in the beginning instead of using the other formula :)

[jwillandcojay]

can you do one that has something like the integral between pi/4 to x^2 of sin^2 (tan t) dt? Im a little confused about it.

[patrickJMT]

@RelativisticVeocity ah, i like that!

[Romis008]

Could somebody please explain why the 1/2 dx became a 1/2x after integration?? Sorry if it's a stupid question, I might just be having a brain fart

[paa3617]

@Romis008

What is the derivative of 1/2 x?

[NguyenEmpir3]

Good thing about video is that you can reply it.. yes.

The biggest problem for me is following the professor.

[malaik9]

omg are ya a guru,cos ya need to get some creds for dis awesome stuff ya doo,thanks a span man

[laithiq91]

At 3:30 why did the one got cancelled?

[antis0cialist]

@laithiq91 1 - 1/2 = 1/2 So it's not truly cancelled, just simplified.

[laithiq91]

@antis0cialist Thank you :)

[alexmusicgraffity]

Is there any abbreviated form to integrate (sin^12x cos^16x dx), source: my hw :/

[MultiMoe91]

thank you for the video patrick..

but i gotta ask.. in different trigonometric techniques of intergration.

aren't we suppose to use by parts instead of U substitution?

[daemonpacman]

PatrickJMT:  Turning shitty students into geniuses.

[shapeurmind]

@daemonpacman that would be his motto :)

[ItsJad]

At 2:40, why didn't you use the trig ID that says (1-cos^2 (x) = sin^2)? Is it because we have a 2x in our cos, and so cos^2 (x) + sin^2 (x) = 1 is only used when it's only an x in front of cos or sin?

Thanks

[Skara555]

@ItsJad also just asked myself the same question?

[Jukoe08]

Patrick What do you do if it is a definite integral?! At the end i just plug in for the postive powers of sinxcosx at the end i plug in pi/2 into the x's?

[swimmerd714]

the antideriv of cos 4u is not sin 4u, it is (sin 4u)/4

[lilcesarboi]

i dont get where the one half in the first example ecame from..

[khwezi1986]

thank you think you should be Dr. or Prof. Patrick JMT

[Capita717]

Just wondering why when you had the integral of 1/4(integral) (1-cos^2(2x)dx you couldn't have changed the 1-cos^(2x) to sin^2(2x)

[HOTSHOT226]

the one minus the one half will cancel?.... wtf

[djisomatic]

After watching your videos I have one major and serious regret---I regret not knowing about your videos my freshman year of college. If I would have, I would've done a lot better. You're a perfect teacher. Thankfully I have your videos at my disposal entering my sophomore year. God Bless

[Falloys1]

Patrick you are the best!!!

[hurryupche]

radd

[fionaNESS]

you should use the fact that (a+b)(a-b) = a^2 -b^2

[1170Nino]

You are AMAZING! lsn if ur interested come to UAE - dubai and teach at a school called al mawakeb school in barsha. ( girls' section) (GOOGLE IT)

WE NEED YOU!

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[TheYorski]

great.......



[escapetocalifornia]

this is how im studying for my ap exam in 2 weeks...

THANKYOUSOMUCH

[jiamonx2]

you helped me out better than my prof did

[ajpl08]

ULOL!!!!!!!

[absmaninga]

2:25 can't you just make it (sin2x)^2,then get the integral of that?

just asking

sorry if i'm wrong

thanks for all your help patrick

[0103lntlts]

at 1:51 use difference of squares formula!

[skyapple92]

thank you so much,now it will be easy for me to finish my homework...

at 5:28 why at the second step written 1/2 dx...then later at the next step it became 1/2x....

but seriously this video help me a lot.thank u =)

[BESTOFBOND007]

hey patrick...in the first sum try multiplyin n dividing by 4....

[quiquemoranmoyano]

Only 40,000 views? that shows how very few people take math seriously. I am thankful for patrickJMT because he makes this blurry vision of Calculus a lot clearer.

[Zadamanim]

@quiquemoranmoyano i would think its cuz ppl dont consider youtube a learning resource

[ovandocarter]

why did we take out one half

[shirleybreeze]

why did u cancel out the 1?

[floydreyplando]

whoa! thanks to your vids. i able to pass last 2 exams in calculus 2 because of our vids. thanks alot. haha.XD

[patrickJMT]

@adolho1 so don't do it! that will show everybody just how bad ass you are.

[EatShanklish]

On the part where you were integrating Cos(4x), cant we integrate it as Sin(4x) / 4? Which will end up the same but just skips the "u-sub" part. Right?

[lossfabio]

Amazing ...from Fabio Brazil

[emilvl16]

hi sir,,how does the 1-1/2 will cancel out,,,?

[lllUSlll]

@emilvl16 hey ummm here is how they do it

( 1 = 1/1 so therefore, 1/1 - ½ = 2- ½=> ½ )

[orangeman9]

At 3:27 you say the 1 minus the 1/2 will cancel. how?

[orangeman9]

@orangeman9 nvm i just got it.

[entrevu]

anti-derivative of cos x = - sin x isn't it?

[patrickJMT]

@entrevu no

[TheCoolfez]

@entrevu

here is a easy way to remember the derivatives

just know these 2.

1. sin -> cos

2. cos-> -sin

now you know that, just change the signs for the other ones:

3. -sin->-cos

4. -cos->sin

now when you want to do anti-derivative, just go backwards, so anti-derivative of cos x is sin x according to rule 1

[thenineminus1]

@patrickJMT thats the derivative

[MEelillitas89]

@entrevu -sinx is the derivative of cosine..the antiderivative of sinx is -cosx

[1521Cme]

@entrevu derivative of cosx-sinx

[xvinesatutube]

@entrevu

no, that's it's derivative.

[EpicWin1337]

@entrevu you are thinking of the derivative of cos. The Derivative of cos is -sin.

[khwezi1986]

@entrevu no its positive sin x

[Kratos0909]

@entrevu u got pwned

[jenniferru]

@entrevu no, dont get confused, the derivative of sinx= -cosx

[Veyronp87]

@entrevu

think of it this way, the derivative of sinx is cosx so the anitderivative of cosx is sinx

[Kr3wOfGa]

@entrevu that's just the plain derivative. The anti-derivative of cos x = sin x. And then if you take the derivative of sin x = cos x.

[billybobbroseph]

patrick my negro my teacher for calc SUCKED got a 55 on my first test and then i started watching your vids instead of going to class. got an A on my final and passed the class with a B+ thanks brahski. true story

[JaiR209]

I know that many people already said this but you literally got me through calculus as well. I learned a whole chapter in 1 hour thanks to you.

[hasben0]

Patrick you got me through calc 1 and im still relying on you for calc two so please dont stop making these videos they are so damn helpfull.

[uponthedownside]

can you just replace the 1-cos^2(2x) with a sin^2(2x) ????

[xingnotzing]

Professor Patrick, your teaching is godlike!

[SlugTruffle]

Just wondering, isn't the u-substitution for cos(4x) a little unnecessary? I think answer is pretty obvious; it seems like it's over-complicating things, idk. But thank you for your tutorials!

[anthonychemistry]

i watched all your videos,, your justmathtutoring website is always pull up in my browser. I recommend your website in school that I a teaching. Thank you patrick.

By the way, You have derived some of the formula in trigonometric identities. You have derived the Double angle perfectly... My Question is Do you have a technique in deriving the HALF ANGLE FOR COSINE^2 AND SINE^2.

Thank you patrick...I am writing your WEBSITE LINK in the black board in the everytime I teach in the School. Thank u

[kojelja0]

very thank u!

[Cybernetic]

hmm just mentioning that you can just take the antiderivative of cos(4x) which would be sin(4x)/4 although u sub will still give you the same answer just a thought..

[shehabTV]

thanks man

ur gr8

[ShiroKage009]

when you were at 1-(cosx)^2 why did you not replace that with (sinx)^2 and then maybe continue with a substitution or something?

[CrabtreeGuitar]

2:50

[sebastiance02]

eres el mejor baby

[IWANTHOTDOG]

no one is as awesome as you are on youtube

[padzman91]

youtube is made for patrickJMT!!

UBER THANKS DUDE! :))

[masterchief377]

Thank you man. I needed this so badly.

[goirish009]

thank you much!!!

[anji0san]

ur awesome Patrick

[Silentshadow664]

how are there only 17000 views, it's the greatest!

[FUCKYOURMOMINTHEASS2]

can you imagine the years before youtube, how people learned calculus II? Boy are they missing out

and do you wonder what the future holds, the students in the future are going to look back at these videos and be like "wow these kids are missing out"

[omarein]

billion thanks! :D

[Mariosklant]

you are a mazing. i'm subscribing.

[isb123]

Patrick, the math maker. I am glad I met you. Oh, yes, thanks a million.

[reenstar22]

you're my savior!! thank you! ^^

[Liz1086]

Extremely beneficial. I have been terrified all week about my upcoming test because I have no idea what my teacher is talking about 95% of the time. These videos have definitely clarified what my book and teacher cannot. Thanks!

[vd853]

this is soo much clear than my professor. All I see is her back blocking the problem while she's trying to solve/teach it...

[And1Allstar08]

Thanks a lot Patrick, I really appreciate your help on everything man. The way you explain this stuff is so clear. Other professors make this stuff that's supposed to really be as easy as you show it, hard as hell!! Thanks again bro and I will keep watching your great videos

[aboveall0006]

whoop whoop, PATRICK FOR PRESIDENTT ahah thanks man!!!

[260209]

making so complicate .... cant u use simple way ,,,,,,, as i think its very very easyy .......

[DiANEoKiKUCHi]

thanks, i was up all night learning all about calculus with all your wonderful n detailed videos :) u r so much better then lots of college prof. who teach this =). do u teach cal at a school? they must b lucky to have ya as i teacher, once again ty

[spacekillers123]

Patrick, all I can say is THANK YOU SOOOO MUCH!!!!!!

I'm not joking, you are a great teacher. Calculus is hard, and trig. sub. is even harder, but you make it seem simple and straightforward.

Thanks again :)

ps. would you be make more videos? I think everyone would love that. :)

[tony225]

Go to his web site and you will find he has videos on pretty much every topic you'll cover in Cal I and II and then some.

[Grobannela]

Patrick, thanks to you and some other videos and material (but most of all, THANKS 2 U) I didn't fail my exam. Now, because I passed two tests, I'm able to do a final one, which is very important to move on in my career.

Once again, thanks for your tricks.

You're an amazing teacher,

=)

Saludos desde Buenos Aires, Argentina!

[patrickJMT]

glad i was able to help : )

[MrTrykster]

@patrickJMT

haha no way i'm from BA too and i'm doing exactly the same exam in 3 days ^^

[crescent11]

A big thanks for the time to supply these vids. These and your site have been extremely helpful. Only -ve comment is the distortion when you speak to loud into your mic.

[patrickJMT]

yea, i agree the audio in a few sucks.

i think i have that fixed now, and it should not be a problem in any more of my future videos.

i am learning the technical side of production making these videos : )

[syriankid4ever]

Thanks a lot this really helps.

[superfichi]

maaan, thank you so much!!

[abaraimido]

A Math Teacher From heaven

[FistsofVengeance]

deeply appreiated

[system0sys]

i use t not u do derive ! LOOL

[NinjaTurtle88z]

excellent information served with a pleasant accent

[RealAgentOfSHIELD]

These videos are great, but I'm a little confused why the final du was 1/4 instead of 4?

[unfillecommemoi]

u=4x

so du=4dx

and dx=du/4

he's trying to find dx directly, so he doesnt have to multiply the integral by 1/4 later on.

[ImbecilicMoron]

BAHAHAHAAAAA! "out front!"

[SaMatta87]

If it wasn't for this video I'd be failing calculus II and be way behind. I'm just glad this is the last math course I have to take for the rest of my life.

[granadaza]

Thank you, you make it simple.

[Ren520]

the foil can be excluded because of the algebra

a^2-b^2 = (a+b)(a-b)

so

instantly,we knew it'd be 1-cos^2(2x).

great work! =]

[saltlife85]

Great example

[prevail5701]

Thank you so much!!! I couldn't figure this problem out.

[dreamonlittleman]

how did u get 1/32 ?

[personnedelanuit]

1/4  X 1/8

[ellimist14]

in step 4 wouldn't

1-cos^2(2x) be sin^2(2x)?

Seems like it would make it easier

[gremlinextreme101]

yeh i solved it that way as well

[manoj0072006]

wow my professor get 70K$ but do not how to teach ...........your are the best of the best ......use of different color make me soo happy ...you are on fire dude keep up good work

[colombiantom]

dude question out of the topic ...which cal is hardest 202 or 209?

[patrickJMT]

i will go with 209 cause that number is bigger.

[HappyVraal]

@patrickJMT lol, thats an awsome response to a question when its impossible to know what the class numbers represent seeing how they are different for each school

[omarofuae]

@patrickJMT LOOL!!!!

[karineattar123]

@patrickJMT

LOL

[5iftyse7en]

dont you need to integrate 1/2x aswell??

[JiGsAwMoFo]

1/2x was the integration of 1/2

[reyn589]

a long solution... is there an easier way like sinx * sinx(cos^2x)*dx

[patrickJMT]

yes, there is some identity you can use to speed this up. i know this works though, so i have never bothered to think about it anymore : ) however, feel free to play with is and get back with me! : ) as erdos would tell you: this is a $1 question