Trigonometric Integrals - Part 6 of 6

[Bbitalokaa]

Hey Patrick! I believe you made a mistake in the first problem.. you have two minuses in your answer so you should get a positive 1/2cos2x! Anway thanks for posting these videos up they were extremely helpful! :)

[stfrankies240]

am lost in this part 6 patrick

[VKM7md]

I don't go to classes, watch your videos and get good grades on my tests :) thank u!!

[patrickJMT]

@VKM7md :) go to class.

[Transpacity]

@patrickJMT patrick isn't the hero youtube needs. he's the hero youtube deserves.

[AliveDog]

Watch Patrick videos

Drink lots of coffee

Study study study

Profit!

[Angelgrrl04]

So this last part of trig integrals is basically for any problems that you wouldn't be able to approach using the other five steps without doing some trig identity or algebra first?

[jong2027]

thanks patrick!!!

[ricky23i]

Patrick

you make calculus 2 look like 1+1=2!

thanks

[patrickJMT]

@ricky23i you are very welcome :)

[LeeRyuuji]

Others multiplied cscx + cotx / cscx + cotx instead of cscx - cotx / cscx - cotx.. and the answer will be -ln|cscx - cotx| + C. Are they the same?

[ALLaboutIBO]

For cscx, can I say that since {csc^2 x = 1+cot^2 x } I could just substitute the sqrt root of 1 + cot^2 x which equals cscx, then find the integral of that? Thank you.

[wzmalik]

i realy learned alot 4m ur clips......ur all 6 of parts of Trigonometric Integrals r realy v helpfull......thnxx a lott .....keep the gud work up.....:D ...thnx

[HouseMuzik4Life93]

Thank you, Patrick, you are a wonderful individual

[patrickJMT]

@HouseMuzik4Life93 only sometimes ; )

[lintingche2012]

For the integration of Csc(x)

why can't I just differentiate it as 1/sinx

than let u=sinx

and integral (1/u) = ln(u)

ln(sinx)?

[blyxx86]

@lintingche2012 Because du in that case would need to be cosx, which wouldn't exist.

[xxqqzzaa]

@lintingche2012 because if you let u=sinx,

du=cosx, but you dont have cosx in the numerator.

[patrickJMT]

@lintingche2012 what about the du? you should rewatch u-substitutions. according to what you are saying, integral of 1/(anything) = ln(anything). take the derivative of ln(sinx) and see if you get csc(x); if not, something is wrong (and it is!)

[mortera340]

@lintingche2012 if you let sinx = u, then it follows cosxdx = du, but u dnt have cosx in the numerator.. if the given is cotxdx the answer will be ln(sinx)

[Gazzawey]

what about if have a square root in the problems ?



[Josh3K]

Thank you so much :D You saved me from bombing my first quiz in Calc 2!

Great series of videos!

[yakimora]

Thanks man..

your videos are really helpful..

I hope they will help me in my calculse II course

[atticus2u]

@yakimora how are you in calculus 2 if you can't even spell it?

[yakimora]

@atticus2u

it's a typing mistake man!!

[atticus2u]

@yakimora strugglin man!

[SwallowThePlanets]

you are the fucking boss

[christinajl]

Thank you, thank you, thank you. Merci, merci beacoup, beacoup. Gracias, muchas gracias. Xie, xie. Danke, danke. Un gros bisous.

[MrTalentSubber]

You're the man... it's awesome that you do this just to help people out!

[Musiclo0ovee]

***** PATRICK IS FROM OUR DREAMS *****

[TheAYRABjackass]

THANK YOU SO MUCH MAN YOUR A LIFE SAVER!

i hav a midterm tomoro and i dont know what i wouldve done without you

so from the bottom of my heart i thank you man!

[gojaysgorush]

Ah Stewart..

[jiamonx2]

for the first equation of this video didn't you forget to make the [cos(x)]^2 / 2 positive instead of negative? because the negative only applied to the ln but you forget for the second part?

[vplof]

So does it work the same way if the exponent is negative?

[trudal987]

Do you use Calculus 6th ed by James Stewart? I always find your examples in that text.

[kenniconnieamy]

How is sin(2x) same thing as 2sin(x)cos(x)?

-Confuse college student D:

[atreyukicks]

@kenniconnieamy It's a Double angle formula from trigonometry (aka 536 math....grade 10 or 11 math in the usa i think?)

[No4sinper]

Thx a lot for these videos I will be watching these over and over again in order to learn calc..KEEP It up Honestly Thank you very much ur a life saver! at least for a dumb person like me

[TylerJMorrow]

Is the technique you used for solving the integral of csc(x) the same technique you would use for solving the integral of, say, csc^5(x)?

[sam1209]

hi patrick, i know u dont like doing homeworks but do would u write my midterm for me and ill pay u in trident splash gums :)

[mypinkdollprincess]

Thanks, Patrick for showing me the trick to integrate cosecx. I "promise" to remember the trick you used and show "somebody" taking calculus so they'd find it useful too. Oh and I won't forget to send your youtube link to their inbox! umm..a little something on my part to spread the "math gospel"!! hahaha

[raiseofdragons]

Greetings from Bangalore India!!

Jaydevi Naren here... really loved the teaching's

i hav my 12th grade xam cming up and was finding it really difficult to keep up with integration.thanks to ur video's i am now able to get hang of integration (hopefuly i do my xam well) !

apart from difrrenciation (which i find it way easier then integration) definite integrals was really mind boggling. thanks to ur video i now understood the concepts.. keep up the good work prof. and help ppl like me... :)

[danielarmenio]

Thank you very much. From Portugal. Wish my professors teach like that.

[JdkParkour]

Why do you dot your "i"s in some videos, but not others =P

[lilangel0072]

do integral for (cosx)^6 and have fun with that shit.

[pjhay210]

how about when you use a inverse trigonometric formula .?

[sinuorette]

Hi outstanding teaching i think im going to love trignometry coz of ur videos..

just a qustion is it possible that we take out the( (1_ cos^2 x) /cos x)..??

[blinkfangirl]

i have a question for you: i understand how to integrate when i see it done, but i have a problem identifying which method to use. is there a trick to figuring it out?

[ny1fanta]

you should really do integral sec^3(x) dx, this problem is so fun, and good for the future viewers.

[krnkid08]

So how do we know how we would simplify a trig function?

for instance how did you know to multiply top and bottom by csc(x) -cot(x) when integrating csc(x)?

[duberryo]

Have you any videos of Integration of sec ^3?

[Christiane0518]

thanks a lot.. ./

[tatfr0guy]

the second one was lucky lol. never would have did that in a million years haha

[WhoStoleMyKiwis]

Usually professors half the time in college never take the "TIME" to go out of their way to do random problems, atleast the ones I know. Thank you so much for taking the time out of your life to help others who are less fortunate of having good professors. I commend your work.

[Eyqp2]

appreciate the help man.. Iv been struggling for days trying to understand but your 6 videos really brightend me up. Thanks Alot keep up the great work

[sandform]

Do you have a video showing how to find the bounds for definite trigonometric integrals?

[hifhif123]

Is the answer -Ln[Csc[x]+Cot[x]] also correct...

I multiplied top and bottom by Csc[x] + Cot[x] and used that as the u sub

[ranidayz09]

This is really helping me understand my online Cal II class...thanks for being so smart and able to explain things better than my book!!! :)

[jlove5113]

@ranidayz09 Same here!! THANKS

[andi039]

you forgot to distribute the negative sign in the first example. when distributing -[ln|u|-u^2/2]

[kgbmonthly117]

I love your videos and I do mean to give a donation sometime, but in the last line of this video's math, I think it should read, ln | cscx + cotx |, right?

By the way, you are welcome to visit Providence, R.I. anytime : )

Thanks for the help this past year.

[1Enuma1]

how did 1-u^2 / u become 1/u - u?

am i bit confused.. T_T

[adrienspawn]

@1Enuma1 You can split the numerator (top) in two, both divided by the denominator, , so 1/u - u^2/2, and that last one is basically u, so you wind up with 1/u - u.

[lestrokes]

@1Enuma1 because (1-u^2)/u can be split to make 1/u - u^2/u, which can be simplified to give 1/u - u

hope that helps!

[victorsandoval7]

cant you do it the other way? like: cos^(2)x sin^(2)x sinx dx??? just asking...

It does look easier this way, but I just got a lil confused.

[victorsandoval7]

I meant, cos^2(x) tan^2(x) tan(x) dx

[mrslollypopify]

yes i really thank you coz now i understand trig intgrls i'm sure dat i'l pass with high flying colors thnx 2 u sir...I LOVE YOU

[rinnarocksdiamonds]

for the first problem, can u change -ln lcosxl to ln lsecxl ?

[Olumaintain900]

@rinnarocksdiamonds should do

[RomeoAngelo]

Patrick, is the following a possible answer to the last problem:

(If not, why?)

(1/2)ln|sinx|+(1/2)ln|cosx|+C

--P.S. Thank you so much for these videos. I hope you have videos on material that is covered in a Differential Equations course. :)

[Rohan233]

The first integration loox sexy

[gam3fr33k]

do you take requests?

[JarOfBuckeyes]

This really is pretty terrific, man. I haven't looked much to see what other videos you have going but I hope that you have lots of calculus 3 (multivariable) stuff available!

[13loodLust]

see at like 5:15 I would never have thot to multiply the top n bottom by cscx-cotx...

[yyourfacee]

Are there any videos with tutorials of integration involving INVERSE trig functions ?if not, that would be so nice! good stuff, keep it up!

[spellmaster91]

5:40 -- I just realized that there's a rule for the integral of csc(x). lol. I guess your work is just the proof.

[skyfaze]

somebody just showed me haha nice one !

[kerkdeng]

thank you for this video..hopefully you give a deepest explanation and example

[blacksmit049]

Most Impressive from 1 to 6, it is nicely done

[spani77]

1/u-u^2dx at 2:15

[chichoboss]

1/u -  u^2/u = 1/u - u

[lilbarlet]

Thank you so much for the help! I have a midterm tomorrow and I have been on your site all weekend! Very well explained and very helpful.

[TheChickenpox]

hey. Thanks so much for these videos of yours.. :D

[syriankid4ever]

Thanks again.

[bnssapp]

for the second question, u know to multiply top and bottom by csc(x)-cot(x).....thats not solving the problem..csc(x)-cot(x) IS ALREADY the answer.. since u already know the answer..this is just a proof

same thing for [integral sign] sec(x)dx.. if u multiply top and bottom by sec(x)+tan(x) = z, and after integral u will end up with ln |z|+C = ln |sec(x)+tan(x)|+C...and this is a formula from the textbook

if theres no way to get that, do we have to try all possible combinations to get answer?

[Lllosiu99]

csc(x)-cot(x) is just the answer how to solve this integral, one of the many ways, it's more than a proof. Proof would be differentiation of the result and getting csc(x). How did someone come up with this method? That's the tricky part, but remember you can always use an universal substitution for trig integrals, it works, even though it's computationally harder.

[k0fdark]

Thanks!

[vault2high]

Thanks alot for this series of videos. Very well explained!

[VVats0n]

Thanks a lot Pat, I actually understand Trig Integration now! I have an exam tomorrow and I'm not even sweating it.

[angohead]

thank you so much!

[korrisha]

Dammmmmmmmmmmmmm you make this look much much much easier than the texts and my lecturer why you werent my lecturer I would have been much better off today look out at your email on here got an important message to tell you!!!

[hbquanie]

FUCK!!!! who needs sschool!!!????

[patrickJMT]

u probably

[hyky68]

BURRNNN!

sorry no offence to hbquanie. just j/ks xD

[dmora015]

@patrickJM Roasted!!

[isoman2kx]

Outstanding work Pat. It's so refreshing to see teachers like you that go above and beyond the call of duty. From reading your site it sounds like you stay ridiculously busy and still do things like post videos such as these.

Thanks so much!

[BigT4313]

lol, think after this math course I'm gonna be done with it for a while

[kriskris17]

thanks so much! you are suchhh a huge help! if i didn't have you're videos i'm not sure where i would be in calc right now haha thanks a million, keep up the great work

[herminioamuniz]

Great video, I can't thank you enough.

[patrickJMT]

glad it helps - quality could be a bit better, but c'est la vie!

[Kmwiti]

good work, I was wondering whether the answer should be -ln|cosx| + (cos x)^2/ 2 + c because you multiply by -1

[913718]

I'm Muhammad Athar Imran from Pakistan and i really appreciate your work.Your way of teaching is real good.teaching is indeed a profession that teaches all the other professions.you've really influenced me by your method.Shall remember you in my prayers.Thanks

[patrickJMT]

wow, that gets 'nice comment of the day'! thanks so much for such the kind words. it is comments like this that keeps me posting videos to help out my fellow man and woman! you give me hope still!!!! : )

[patrickJMT]

thanks! : )

[miarmansky]

tebe musi dobre jebat :D

[patrickJMT]

what does that mean?!?!?! : ) i hope something nice! : )

[miarmansky]

honestly not :)

but you are doing a good job.

I am just wondering how to pass an exam on friday,being little bit pissed of it. :)

just continue ;-) good man

[Waranle]

nice video thank you

[patrickJMT]

thanks!