Integration By Trigonometric Substitution

We've got two techniques in our bag of tricks, the substitution rule and integration by parts, so it's time to learn the third and final, and that's integration by trigonometric substitution. This is probably the toughest one, and it only works in very specific circumstances, but when those circumstances arise, it works like a charm! So let's make sure we know how to execute this bad boy.
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[@user-jx8jp5kh6g]

Hi Professor Dave... Thank you very much for this video, kindly assist me on when exactly do we need to draw that right angled triangle ??😮 Is it always when we have the trig substitution or ?

[@lanepotts1046]

Dude this is the hardest thing I’ve done in my life thanks for making it a little easier

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Professor Dave has carried me through Ochem and now Calc 2. If only he did microbio

[@ProfessorDaveExplains]

well i did biology and biochemistry, did you see those? microbiology will be coming soon, maybe early next year!

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This is just awesome. Every single time I felt confused in my college calculus lectures, I come to this channel!! Thanks for making math seem fun and understandable!!

[@gekkouga2828]

Thanks, Professor Dave, for giving a base in doing integration! I am now confident to work out any integration problem.

[@albabelen5628]

did the last exersise perfectly! Honestly, I thought I'd write some short resume I wouldn't fully understand with this video. I ended up writing a whole page with every example and in-betweens you did. I don't regret it, because I understood everything, and I won't struggle to remember it. Thank you so much for your easy explanations! You make integration seem so much easier!

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thank you so much! your videos are really helpful love the visuals and how everything is taught in a concise matter under 20 minutes. i am looking forward to using your videos to tackle on organic chem this school year :)

[@gamerprimeultimaxsupreme2776]

Thank you so much for this. This video has made trig subs a lot more understandable.

[@POPFARRT]

I watched 3 people try to teach these 3 concepts, what you did differently is explain the trig substitution's and identity's. I also like how you did not go to the next step, without mentioning exactly what you did(even if it was small) . Also starting off small before performing a problem Great work.

[@TitaniumSporks.]

My gosh thank you so much for this video. It really made this topic click for me (for the most part, still struggling with back substitution, but I think that's due to how long it's been since I initially learned trig identities)

[@eyoelgashaw5089]

you're a living legend you know that!! my professor tried his best but not enough. If only Feynman was here to see ur tutoring skills. Also i am deeply waiting for your ODE and PDEs in addition to any programming languages. i want to see you in Khan Academy level. having ur own website and all.

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my online class proffesor only reads his presentation and doesn't it that much. Proffesor Dave you really helps me.

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Wow, didn't know cal2 could be that simple. Thanks for your magic!

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thank you so much< i was literally looking for this explanations for so long. so happy you made this video

[@reginalorenorcena7131]

Thank you so much Professor Dave😍! This is a big help to my exam.

[@user-ix7jy5pe1e]

This is really great thank prof DAVE

[@franzjarvybaconawa1082]

Those tips helped me understand trig sub a lot more than before

[@reginalorenorcena7131]

Thank so much Professor Dave😍! This is a big help to my exam in Calculus 2💗

[@curtpiazza1688]

Thanx Prof. Dave! I wish I had you for calc.!

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I wish this video had been around when I took Calc II in 2002 ... this makes so much more sense.

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Crystal clear! Thank you!

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Brilliant concise explanation!

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Bro this did clarify everything, tysm

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Leo Bergmiller Please Professor Dave. Any more material you could release would save me on the exam tomorrow

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Will have a quiz in a few hours thank you for your help!

[@kiraivanova1342]

This is so good. thank you!

[@shahrukhqaiser1745]

(Cos theta / sin² theta) = cot theta/ sin theta =cot theta cosec theta Could have used that too. Thanks for the video. Great explaining. 👍

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this is so helpful thank you so much. wish I knew this channel before

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YOU MADE MY LIFE MUCH EASIER. THANKYOU SO MUCH. PLEASE MAKE VIDEOS ON ALL THE CHAPTERS FROM MATHS HL IB :D

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U made it so easy bro appreciate it

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Thank you for this.

[@knowledgeboy6137]

i thought this is very hard you prove me wrong thank you Professor

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Excelente explicación, usted explica perfecto amigo...

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Wow! I wish I had you for calc!

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had to watch the video twice but i understand it a lot better now

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Professor Dave really knows everything

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just realized the same thing lmao

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Thanks so much for the videos! You should make content on multivariable calc!

[@ProfessorDaveExplains]

i did that! keep going through the series.

[@user-hn1sw6nf6s]

Thanks 🙏🏻 .

[@mosshead_vinsmoke]

I skipped all my cal-1 and anything related to trig's during my highschool and here i am in clg taking maths & computing as major , ive delved in many2 videos and channels and i think your videos are always the best in explaining things and why/how we tackle them down Thank you for this amazing Channel and lectures

[@nerd2544]

another computerfield + math 🔥 i didnt skip but just forgot high school calc

[@EvilSandwich]

Can we just have a round of applause for the poor overworked mathematician that figured out this trig subbing mess centuries ago from scratch with NO help, so we didn't have to?

[@dilanurkok5316]

You are great. I am appreciated. Thank you :))))

[@kashifhussains2951]

May u have all the happiness and peace in ur life💙

[@RadoHudran]

One small correction at 12:00 cos θ/sin^2 θ is equal to cot θ . csc θ which can be directly integrated to -csc θ + C instead of the u substitution

[@wisegamer706]

Not a correction. Just another way of doing it.

[@jkgan4952]

Yo this is kinda cool. I found out that trig substitution is basically u substitution in reverse. Instead of finding the integral of f(x)dx, we find the integral of f(g(x))g'(x)dx. This integral is going to be F(g(x))+c. And if we resub x back for g(x), we get F(x)+c. Pretty neat technique!

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Very educational indeed

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THNKS REALLY HELPFULLLLL

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This video is amazing, I love how slowly and clearly you explain!

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You're a doctor.. because you vanished my tension about this calcus

[@zzzzzzzjsjyue2175]

best vid ive seen on this

[@BobbyC-be9vy]

Very clear and methodical explanation. Just wish he’d use arcsin to denote inverse sine.

[@NewWesternFront]

why

[@jds189]

brain hurty

[@kevinkelly6492]

lmao same

[@yerushaleyim3655]

Thank u..

[@adityaadit2004]

Can I choose x = a cos O for sqrt(a^2 - x^2) instead of x = a sin O ?

[@andrewgarcia9976]

Professor Dave, do you have some sort of pdf version of this whole series that can be quickly referenced? I would seriously pay money for it

[@ProfessorDaveExplains]

I do not but I had thought of that before, maybe some day!

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Your videos have criminally few views, it makes me sad :(

[@ProfessorDaveExplains]

pretty please tell your friends about the channel!

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@@ProfessorDaveExplains Oh I have, but I'll certainly continue to spread the gospel!

[@naseralhamwai7627]

Why did you not take the absolute value of tan& , tan& is different in this case since. -pi/2

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Ditching my college prof and joining the prof dave army✊🏻

[@unusualfrog779]

where does the tan in the denominator in the comprehension question come from?

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Dude no way you made everthing this simple

[@Jake-uo3ne]

If √9-x² was a denominator, what would be the first step to solve it?

[@ijazulhaq6078]

on 7 12 how 1 is change to teta in csc*2 Q -1

[@shaheenbean]

At 8:40, is it a coincidence that "a" on the right triangle was equal to the numerator in the original problem, or is there an actual connection?

[@platysmemes7663]

thanks!!

[@user-yg97f5hfvh]

You might sub x=acos(theta), x=acot(theta), x=acsc(theta)

[@danielalexanderreyespineda1131]

u r fantastic

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Thanku so much sir🙏🙏

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totally agree!

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[@joshuareyes1560]

I thought I worked out the last problem wrong as everything cancelled, but I'm glad I did it right xD Great video! Saved me for sure.

[@vix2740]

6:17 why do we bring theta up into the solution of dx/dt

[@yamkelabalisa7330]

but why \int \:x^3\sqrt{x^2-1}dx is not working?

[@Divine_Discoveries]

toughest video till now, but i completed it

[@elamvaluthis7268]

Great professor 🙏🙏🙏.very nice explanation 😁😂😂.

[@TheSkilledTroll10]

Do you have integration by partial fractions

[@siausoonhong6905]

Best Ever

[@SodiumOverdose]

thank u goat

[@maimomirabel2685]

I have a worry here the numerator has 9 and x^2 substituting x from the original function was thinking u will just substitute in the given function as it is

[@letslearnmathematics5432]

Can't use power rule?

[@AS-is2di]

Grigory Perelman! Is that you!?

[@rabia8877]

Weldon sir

[@aashsyed1277]

0:46 5 actually

[@aashsyed1277]

Ill give you 1 million dollars for this. Thanks.

[@user-jz8kn6tl6i]

Dear Proffessor cant we use x = acosθ instead of asinθ?

[@AV4Life]

Technically you can, but you’d have an unnecessary negative sign to deal with. It’s better to use sin.

[@neo8352]

2:18 Why that(cos theta)has to be absolute value?

[@RazorM97]

0:55 "a can be any positive number", and x or the theta from the cosine could have been negative

[@Localpref416]

How do you get the 1 for a^2 - a^2 sin^2(x) = a^2(1-sin^2(x)). How does that simplify at all?

[@sactornogaming]

You factor out a^2

[@topapo3661]

1-sin^2(x)=cos^2(x), so it becomes a^2 cos^2(x), whose square root is a cos(x)

[@beegil911]

man this thing is hard

[@beegil911]

its like nightmare

[@CoderSV3]

12:38 What happened to the cos theta d theta?

[@topapo3661]

doing u substitution inside of trig substitution