Hyperbolic Functions - Integration

[@fsxaviator]

it might be worth mentioning for the problem at 1:40 how the sinh(x) is disappearing. We're replace dx with an equivalent expression in respect to u. So in order to do that we solve for dx and get *dx = du / sinh(x)*. Then we replace dx in the original integral with that and we have u^2 * sinhx * du / sinhx, and the two sinhx's cancel each other out, so we're left with just u^2 du. btw thanks patrick for helping me pass calc 2 11 years later!

[@102293]

He has a gift that many teachers dont have. The gift to make it interesting

[@jamescboyd]

Appreciate all your videos!!! I'm taking Calc2 online and so far it's killing me. But I will prevail! (..and you'll help me do it.)

[@mamadetaslimtorabally7363]

Always great to watch your Maths videos Patrick. Thanks a lot.

[@oglow100]

haha i love that you made a playlist for calc 2 and that is the name of the course im doing. Easiest subject to cram right now :D

[@antonpascua8795]

Ur trig identites at 6:00 is wrong. its sinh^2x + cosh^2x =1

[@MrFrankthetank0000]

We are using James Stewart 7th edition in my college. You're correct Hyperbolic functions are before integration by parts and I believe this is Ch.5 in your edition. It is Chapter 6 in the 7th edition. Chapters 6-11 are Calc 2 in my school. Studying now for Calc 2 next month. Sweating balls over this stuff :/

[@harjotrai2429]

Swizz Beats Nope. The identity is cosh^2x-sinh^2x=1. Hyperbolic functions are a little different with signs and whatnot from regular trig.

[@ZXC-ey3zu]

I got 3 of it without looking into the solution. Our prof is the best AHHAHAHA.

[@Lien-wx5mb]

patrickJMT is the baeee

[@DoggoWillink]

@MaqOBak This is usually the last specific integration chapter before Taylor polynomials and infinite series get introduced. After this you know all the Calc 2 integration techniques, except using series to approximate hard integrals.

[@Elk9]

Your lesson was easy to comprehend, thank you.

[@KalCrazyFJ]

Patrick Sir, What if we have to find the area enclosed by a hyperbolic function? How do we find the area? Is there any video on that? You are great Patrick. Keep up the good work.

[@ashmanwalal]

hey i was just wondering if you could help me with this question. calculate the integral of square root 2x^2+4x-8 dx they use hyperbolics in the answer. thanks

[@MsEady123]

That's for this video. My book doesn't show how to use the integrals hyperbolic. My book is trash lol.

[@shhh9162]

Rahul Rahul who’s gna tell him that some books actually are bad at explaining something that shouldn’t be that difficult by using confusing notation and assuming the reader will understand without adequate explanation???? man said “never call a book trash” ... i have to laugh

[@cc11rocks]

Finding the area under a curve, you would take the integral. Wouldn't this be the same for a hyperbolic function?

[@mohammedmm9685]

thanks

[@carolinagranados8256]

You're a great techer! thank you!!

[@NurAisyah-pc4uu]

Did you used calculus by james stewart ?

[@patrickjmt]

not the toughest in the world : )

[@IntoTheSettingSky]

How would you do a definite hyperbolic integral? [sinh(2x)] / [cosh(2x)] from |.5 to | 0. (top to bottom)

[@ghuss514]

Hi Patrick, do you think you could demonstrate how to proof the following: integral du/sqrt u^2 +or- a^2 all equal to ln (u+sqrt u^2 +or-a^2) +c. And thank you so much

[@Bludgeoned2DEATH2]

The derivative of cosh is sinh? >.> no more negatives?

[@viktorchao4191]

Thank you very much. It really helped a lot.

[@perpetututuator]

THANK YOU VERY MUCH

[@EngrAhmed9]

will u provide contact

[@patrickjmt]

@Charliek2003 ha, i live on youtube.... always just hanging out, boring people with math...

[@aishamadondo8636]

wouldn't the quotient rule work instead?

[@DoggoWillink]

@MaqOBak No I'm wrong, partial fractions is after that. But your comment is old I didn't realize that, sorry you probably know by now.

[@Lucerozeus]

awesome video. just one question though. my professor had the negatives in the left hand side of the equal sign for sechxtanhx, csch^2x, and cschxcothx. is it the same thing if the negative signs are in the right hand side of the equal sign for these hyperbolic functions?

[@JoshauCalum]

+Byron Lucero yes, consider the negative sign as (-1) which will remain constant through integration.

[@Cowboy_Barbey]

Thanks for your help!

[@aminariaz3639]

Whats the integration of coshx/x???????

[@MaqOBak]

Guys what video would you suggest to watch after this regarding integration ofcourse?

[@LeoIsMyNameYo]

can you do a video on laplace transform explaining from basics to advanced stuff?

[@patrickjmt]

+Rishav Roy i have stuff on laplace

[@AmeerulIslam]

isn't sin^2(x) + cos^2(x) = 1 , why cos^2(x) - sin^2(x) = 1 in this video? is sinh x and sin x different?

[@AmeerulIslam]

also is it hyperbolic or hyberbolic?

[@dylanrambow2704]

Ameer ul Islam Hyperbolic. And yes, sinh(x) is different than sin(x).

[@alexgaming3285]

Thanks sir ❤️

[@bobbylee08]

WEll done!!! better than my prof... -_-

[@Ians2910]

Can you explain why the Derivative of Cosh x is equal to Sinh x instead of -Sinh x??

[@dianneperico]

Because it's in hyperbolic. Some of Hyperbolic formulas are kinda different to simple derivatives formulas I believe.

[@skvstheworld]

Midterm tommorow...thanks so much!

[@jackobite1000]

can you do some on integrating functions like (1+x^2)^3/2 where you have to make U a hyperbolic identity??

[@gelly2342]

cosine and cosh are different... but all good otherwise! hyperbolic cos is just said as COSH, sinh just as SHINE, tanh is just THAN (pronounced with a F, like Ftan ). :D

[@anouar4habbo]

patrickJMT Ill tell every Body About You you're amazing if only you could translate what your doing to french and arabic :) you will be the world math teacher :)

[@AnkitKumar-cr3qs]

Hii sir... thankyou so much I am from India....please make videos on polar representation of complex number

[@patrickjmt]

i already have

[@aLxies19]

why did the denominator became 1 in 3:40 ? sorry for the question -_-

[@eveee4449]

thank you very much

[@rag2574]

hey thanks a lot it help.

[@majidhesami4812]

Thanks a lot. I have one integral that I dont know how to do it. Int( exp(-x^2) * [ sech(bx) ]^2 ) . thanks in advance

[@HussainAlAlwan]

I love you man

[@oneinabillion654]

Doing A levels now but still bashing through ur calculus videos :D

[@GioMaretti]

int: sechx? is _arctan(sinhx) + c_, but I get is *2arctan(e^x) + c* I DON'T KNOW how get it....

[@NotYourAverageNothing]

sech(x)= 1/cosh(x)= cosh(x)/cosh^2(x)= cosh(x)/[1+sinh^2(x)] Do u-substitution with u=sinh(x). Tah Dah!

[@sherilove1987]

Hi there thanks so much.but I don't seem to understand how you used that method( u- sub) seriously

[@akshitasingh6293]

im crying

[@cc11rocks]

Is not reliable. Check out CDZA's "Fresh Prince of Bel-Air" translations. That'll show you to use Google Translate (I use it myself for certain items - just not a good idea to translate blindly using the tool)

[@MaqOBak]

Hey sorry, i did look at your previous comment and it kinda help but i forgot to reply. Thanks anyway

[@KyleJosephSanders]

hyBerbolic? twice?? once on the white board, once on the video title... soo phunny.

[@JoaNYC]

That left hand is highly frustrating

[@faithelias2798]

God loves you all

[@---ly4se]

the u-sub is way easier, i wish he showed that

[@patrickjmt]

if i was rich, i would hire people to translate them :) but i am not

[@anouar4habbo]

Someday you'll be Rich

[@HotPepperLala]

Someone tell Patrick he spelled Hyperbolic wrong lol

[@ttfan94]

google translate ??

[@ckoreanman]

The derivative of cosx is "-sinx" not sinx

[@harjotrai2429]

Nah dude, this is hyperbolic trig, not regular trig. derivative of coshx=sinhx. No negative.

[@5cbnkd]

Antiderivative? Don't you mean Integral...

[@alanl9497]

5cbnkd It's the same thing.

[@MarkMcDaniel]

Integrals ARE anti-derivatives, given that the steps to integrate were reverse engineered from the steps to derive.

[@ebrahimreda6209]

يسعد دينك