Integrals: Trig Substitution 1

[GenericCoder]

Why is the integeral of d(theta) = theta can someone explain this please ?

[natdogrocker]

@GenericCoder its the same if it was integral of (1 dx) that would equal, as per power rule, x. same thing with theta

[GenericCoder]

@natdogrocker

Oh I see thanks alot dude. that makes sense.

[GenericCoder]

Can't we solve this by reversing the product rule ? 1 * (3 - 2x^2)^-1/2. then doing the way Sal solved for it before ?

[GenericCoder]

Man your really awesome thanks alot. I wanted to ask one thing Can't we solve this by reversing the product rule ? 1 * (3 - 2x^2)^-1/2. then doing the way Sal solved for it before ? I didn't try it yet,but I will after watching this video.

[phantomofsunshine]

WHOA YOU'RE MAGICAL! thank you

[Germs9592]

you've saved my buttons once again :D

[saftiani]

kereennnn.....

[jajisaeklfe]

How can you just set 2/3*x^2 = sin(theta) when they are completly different things? 2/3*x^3 can be any real value and sin(theta) can only be max 1 and min -1??

[Prolocater]

@jajisaeklfe he set 2/3*x^2=sin^2(theta) not 2/3*x^2=sin(theata)

and the reason he did that was so he could solve for theta and x respectively faggot

[Prolocater]

@jajisaeklfe he set 2/3*x^2=sin^2(theata) not 2/3*x^2=sin(theata)

in order to solve for theta and x respectively faggot

[philster00700]

uber hacks....good job Khan

[Romis008]

this just blew my mind

[conorpatrick123]

@sahiti321 imho, thorough, deliberate teaching is far superior, on every level. If you don't like, pause at the end of the video, look at what he drew, and figure it out for yourself.

[sahiti321]

k... can i tell u somethng? U TAKE TOOOOOOOO LONGGGGGGGGGG to explain simple shit* YOU KNOW.. ppl now-a-days.. do NOT have that much of patience!?? like seriously ... reharse ur self, and make the vid as short, concise, and perfect as possible.. that's the whole idea of learning from a video, if u r too fast, we can just rewind ..

[labeeb786]

@sahiti321 dude ur an idiot. I'm first year calculus and this is helping me so much. We haven't even learned this in class yet and I'm watching ahead to get a small grasp over it. If he did it the way your saying, I would be 500x more lost. If your so passionate about your way go open ur own site. Seriously you have no idea what your talking about yet you still decided to talk. Stop that now.

[AdrianDotis]

@sahiti321 can i tell you something? ppl now-a-days are passing math thanks to Khan's videos. Who the hell are you to tell him how to teach?

[TheXeneize100]

@sahiti321 if its too slow, you can fast forward...retard

[emaster01]

What program is being used here for the math? I would like to start a video series on passing some actuarial tests.

[Blackthunder0402]

thank God for Khan academy. the fact that these are free is the greatest thing ever

[Bumperpegasus]

Oh. Finding a HD vid inside the playlist makes me all happy

[pepteamsergi09]

Nice 1 TY



[MrXwaYZ]

nice snort in the end!! lol.., #dang.... I learn this on senior high school...

[OpenTheTrollGate]

best teacher on the internet

[tamsanh]

I solved for 2/3x^2 = cos2o, and I get a different answer... mine comes out as -1/sqrt(2)*arccos(sqrt(2)/sqrt­(3)*x), which is NOT equal to 1/sqrt(2)*arcsin(sqrt(2)/sqrt(­3)*x). Can I get some help?

[nicoheckens1]

the derivative of sqrt3/sqrt2 sin theta=sqrt3/sqrt2 --costheta, right? Where is the negative sign?

[hvhfyjtdhf]

@nicoheckens1 uhh no. the derivative of sinx is cosx, not -cosx. the INTEGRAL of sinx is -cosx +C



[E90PAT]

SNIFF**

[Andytk33]

@E90PAT DAT SNIFF AT THE END MADE NE LOL SO HARD



[Manoniie]

Why couldn't you just write the function you begin with as: (3-2x^2)^-1/2 ? Then you can fix it without much trouble, or am I wrong?

[Musiclo0ovee]

Sal Sal Sal Sal Sal Sal Sal Sal We love you

[denebgarza]

making vids even when you're sick! thanks Sal.

[tIs4gatorbait]

damn that problem sucks



[xeidy]

was very helpful to understand the ins and outs of the trig substitution :) Thanks Sal!

[risquewebsite]

MATH IS FUN!

[Kmg403]

I'm in a calculus class now and we haven't even done this yet... but jesus you make this look easy!

[SultanSamer]

nice ending =)

[uccvertigo]

Isn't it necessary to describe the domain of definition for x? cause in some cases x^2 might be bigger than 1 so you can't have (sin^2)(theta)=x^2 cause it's imposible.

[Mugwump720]

@uccvertigo In this case I don't think it's necessary, because we are already under the square root. So that means that (2/3)x^2 has to be smaller than 1 or else we'd have an imaginary number.

[shawnvega]

I finally know what to do with theta. thanks :)

[nomadKJL]

Thank you so much! I've spend so long trying to solve a problem similar to this. After watching your video I finally understand my errors. Thank you!! :)

[DrDerive]

thank you :)

[CliveReyes]

I think we can integrate directly as (3-2x^2)^-1\2

Can't we?

[ShadiZ11]

@CliveReyes You can't do that directly. Don't forget that you have a 2x^2 inside the parenthesis. And simple substitution does not work here because you will end up in two variables in your integral. Therefore, the best way to do it is to use trigonometric substitution.

[jazzkingrt]

Sal: The first time I saw the video, it clicked. The second time, I followed along with my homework problem and it works beautifully. Now to see if I can do the next one on my own :)

[3DMilkMan]

Click. Understanding.

[mkcdcf]

Thank you thank you thank you thank you thank you!!! Why isn't there a standard format for teaching???? You have helped me soo much! :-)

[omakar3a]

I'm sorry Sal, I don't know if it's just me but this has been a confusing video :(

I still love you tho

[hatimy]

@omakar3a i was confused at first as well, but go over it n write it down as the goes along. helps me understand a lot better! tanx mr. khan u r my calculus hero!

[zndr27]

is there another way you can solve this?

[recmer3]

now i can actually spam calculus homework w/o using a calculator!!

mad props to you Sal

[aom9010]

thank you!!!!!!

[1001014]

HD!!!!! So good <3

[jeswin7]

Mr khan,

I have a question about the substitution you used. If you had equated 2/3x^2 to cos^o, would this have affected the final answer.

[luislinuxero]

@jeswin7 No, when you solve an integral correctly you get the same result, but sometimes it can be trickier or easier to solve one with trig. substitution. depending on the substitution you choose.

[LineageAlesana]

This makes so much more sense now. Thank you!

[david0aloha]

It seems like there's so much more to this. That's neat that a trig function can be used to find a way to evaluate a non-trig function. Now I want to know why. That seems so elegant... and you show it so well (my instructor rushes through and gives the class about 5 seconds, before most people get a chance to put down their pencils from copying stuff down, where he asks "So is this okay... everyone got it? Good, moving on!") Thanks Sal.

[MrKwanlee]

nice video thanks

[renesisrx8]

This seems very simple for this example but when they throw the radical on the top or add other constants, I get lost.

[odstderek]

this tutorial has been extremely helpful, thank you

[Sukasa888]

dude. you really need to go to vidcon and bitch slap people with your calculus skillz

[heroinkillz1]

I have spent so much time trying to figure out trig sub from my notes and book... I couldn't quite get it until I watched these videos. Thank you!!

[Jonnyistheman9000]

You sir, are a gentleman and a scholar.



[napalm4sd]

Isn't the square root of 3 over the square root of 2 a constant? So when you took the derivative of it wouldn't it dissapear? Its been a while since ive done this..

[laram24]

@napalm4sd No, it doesn't "disappear", because you can take out the constant while doing the derivative then multiplying it at the very end. But, if you would take a constant that was added or subtracted, then it would "disappear".

[Pastafarealist]

*SNIFF* I'm crying too Sal!

I can't believe this stuff is so freaking simple. It's PATHETIC how textbook authors and many math teachers do their best to obscure methods for computation just so they can look smart(even though it just makes them look stupid in reality). How many times have you heard a student say "Wow this teacher is a moron! He can't teach!" and yet that same teacher thinks "Hah, none of the students understand because my method is too smart!"

[orcelb]

*SNIFF*!! :D

[robo2000nitro]

lmao nothing fancy

[nonxcarbonx]

Thanks. When I first read this in my text with the absence of an introduction, I didn't know what was going on.

[yws1991]

With his chocolate velvety voice, khan brings hope to students everywhere!

[lilmaqi]

@yws1991 I like how you describe his voice. Nice. It fits!

[Btwiceborn]

JUST before the video ends.....SNIFF! funny stuff.

great instruction on the trig sub,

[BoppreH]

Way to end the video.

And you are a great teacher.

[Djole0]

woudl be easier if u would 2/3x^2 wrote as sqrt2/3x^2 and then and then just take substitution t= sqrt2/3x^2, and get the solution for arcsinsqrt2/3x^2) + C...

[260191894]

I feel like crying: it is so simple the way you explain it. Yet, in class, it's like grinding our heads on a cheese gratter.

[rinwhr]

Wow, i mean just wow. I don't have to memorize this anymore lol

[hsktoadftw]

amazing!

[FreezingSun14]

brilliant

[imalylime]

thanks sal. my teacher taught us another way with drawing triangles and manipulating the formulas and it totally confused me.

[bullzeyet]

wow i never knew you could do that

[interxavierxxx]

Mr. Sal, what would if you used (sinx)^2 = 1 - (cosx)^2 instead of (cos)^2 = 1 - (sinx)^2 ?

In these kinds of situations, how would you know what to substitute? Is it always recommendable to choose the one that yields an uncomplicated derivative?

[bboydjoe]

wheever u have a sqrt(a^2-x^2), its always better to use x=asin(theta), cuz when u get dx, u wont be stuck with any negatives (cuz derivative of sinx is POSITIVE cosx)

so, in my opinion id use (cos)^2 = 1 - (sinx)^2 instead of the other one, but u can use either way.

[doubleja]

I'm just learning about integrals (and i have a calc final in two days, lol), and i've got to admit that that was the tastiest way to solve the indefinite integral, substituting the trig identity and so forth...

Algebraic manipulation as such is truly an art form.

[Ivan2005]

Man good job explaining this. Well done!!!

[shoesftw]

dude your awsome man

[Pr0x1mo]

wow i would've NEVER come up with that on my own, this is brilliant stuff.

[slickkill77]

You explain this so much better than my college professor. Thank you.

[heroinkillz1]

@slickkill77  DITTO!

[woodenjaw]

Yes, More Videos Please!!!

[Budisawsome]

During class i was wondering how you would derive the area of a circle formula. Who ever came up with this is a brilliant person.

[woodenjaw]

It should be under one of the videos in "Solid Revolutions"

[woodenjaw]

I agree with Thevidfather, you really get a good intuition of what our doing.

[thevidfather]

Hi,

I'm an IB Maths HL student and I've found your videos absolutely brilliant! They cover everything I'm doing in class and are really improving my understanding. I can't thank you enough!

[espen180]

Won't the square root of cos(θ) squared be the absolute value of cos(θ), or |cos(θ)|?

[christopherchubb]

yes it would, I've seen it time and again simplified otherwise which isn't technically correct. Nothing against you Sal, its just something that annoys me. I put an answer in a test in terms of that (it ended up with a |cosθ|/cosθ) and got marked down, I then had to explain it to the teacher to get the mark back lol.

[bboydjoe]

@espen180 and christopherchubb

no, it wouldnt be |cos(θ)| because its an INDEFINITE integral, so u can just drop the abs. value bars.

but it it were a DEFINITE integral, then ud have to check the domain of cos(θ) with regard to the upper and lower limits.