Integrals: Trig Substitution 1

Example of using trig substitution to solve an indefinite integral

[RenzoPereyra]

"I'm gonna do a bunch of these examples so You can get familiar with them."
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* *S N I F F L E* *

[mustangjoe]

I personally think it is easier to rearrange the denominator to be 1/√1-u^2 trig identity:
√(3-2x^2 )
√(3(1- 2⁄3 x^2 ) )
√(3(1-(√2/√3 x)^2 ) )

Let u=(√2/√3) x
√3/√2 du = dx

after elimination the √3 from top and bottom.
integral of 1/(√2(1-u^2))

integral of 1/√1-u^2 is arcsine x

so
1/√2 arcsine(u) +C then plug u=(√2/√3) x
back in and you get same answer.

[Blackthunder]

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

[vidfather]

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!

[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.

[umuter]

ain't no way I'm gonna remember this at my final exam R.I.P to my grades

[Link_]

You don't need trig substitution for this; just substitute u=x*sqrt(2/3) and du=sqrt(2/3)*dx and use the antiderivative of du/(sqrt(1-u^2))=arcsin u.

[lwreltteratgmail]

OMFG thank you!
i was just devastated by my math teacher telling me that we won't learn trig sub this year, and without a teacher it is hard to study stuff you haven't had yet, but now i CAN do it, next year is gonna be a piece of pie!

[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 :)

[disgorgeengorge]

Missed a day of my Calc 2 class because of the flu. You are a life-saver khanacademy

[Bumperpegasus]

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

[recmer]

now i can actually spam calculus homework w/o using a calculator!!
mad props to you Sal

[asquare]

she is an indian girl who is quite envy about the achievement of sal, this guy is perfect, concise and to the point.

[SteveJagges]

This is awesome I have an assignment due tomorrow and my prof did a terrible job explaining this concept. You made it clear as day. Thanks.

[yws]

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

[dorysoldoff]

Great video as always! But, I feel like this integral can be evaluated more easily with a simple substitution and arcsine rule.

[mightyworker]

Sometimes the passivity of watching a video turns off the brain to making even simple connections that it otherwise would easily make. He is simply doing an exemplary job of Not making assumptions about the audience's knowledge which is important when you are teaching using a forum that does not lend itself to asking questions/clarifications. Plus, you are getting a nice review, recognizing that you are actually simply building on things u already know- a nice thing IMO.

[Prxmo]

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

[dezbs]

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!!

[davidaloha]

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.