Integration By Trigonometric Substitution

Рет қаралды 324,645

Күн бұрын

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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Пікірлер: 152

@sunya6654 4 жыл бұрын

Professor Dave deserves our tuition fee. I'm learning effectively to him rather than university professors tbh

@abiyyuyandra1065 2 жыл бұрын

yeah bro

@CHEFWILLAY Жыл бұрын

this is still true btw

@objectoriented3049 Жыл бұрын

Zip up his pants when you're done lil bro

@arthurngosa5926 Жыл бұрын

@@CHEFWILLAY for real no cap

@user-jx8jp5kh6g Жыл бұрын

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 Жыл бұрын

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

@emmacatte 6 жыл бұрын

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

@ProfessorDaveExplains 6 жыл бұрын

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

@melester2728 3 жыл бұрын

@@ProfessorDaveExplains 🔭 ASTRONOMY

@happyjohn1656 2 жыл бұрын

@@melester2728 🔭 ASTRONOMY 2:45 AM (yep!) 2/15/2022

@fahad_hassan_92 Жыл бұрын

@@ProfessorDaveExplains Bro knows everything

@abuabdullaahiwaaaishatah8235 8 ай бұрын

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@rachitagarwal610 3 жыл бұрын

No matter how hard the topic is, his intro makes it all look good!!

@bifengxiao9300 3 жыл бұрын

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 4 жыл бұрын

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

@albabelen5628 2 жыл бұрын

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!

@dakshbadal7522 3 жыл бұрын

If you want him to earn money but can't afford patreon, just watch the whole of the skippable ad.

@bubblesxo 6 жыл бұрын

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 :)

@eyoelgashaw5089 3 жыл бұрын

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.

@reginalorenorcena7131 3 жыл бұрын

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

@gamerprimeultimaxsupreme2776 4 жыл бұрын

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

@jethior 6 ай бұрын

oh my God! it takes me only 15 min to understand what our lecturer hasn't explained efficiently for one year. even here on KZfaq except yours. thanks a lot my mentor!!

@joao-me1zf 2 жыл бұрын

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

@TitaniumSporks. 2 жыл бұрын

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)

@aaronzai 2 жыл бұрын

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

@junisaresilvosa9430 2 жыл бұрын

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

@reginalorenorcena7131 3 жыл бұрын

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

@shahrukhqaiser1745 6 жыл бұрын

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

@shrujalagrawal3743 5 жыл бұрын

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

@user-ix7jy5pe1e 5 ай бұрын

This is really great thank prof DAVE

@johnholme783 Жыл бұрын

Crystal clear! Thank you!

@mryup6100 4 жыл бұрын

This guy is amazing!!! 💯

@kiraivanova1342 8 ай бұрын

This is so good. thank you!

@leobergmiller873 6 жыл бұрын

PROFESSOR DAVE YOU ARE MY HERO PLEASE POST THE REST OF YOUR CALCULUS VIDEOS TONIGHT I HAVE THE AP CALCULUS BC EXAM TOMORROW

@emilyhenegar7320 6 жыл бұрын

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

@curtpiazza1688 2 жыл бұрын

Brilliant concise explanation!

@POPFARRT 2 ай бұрын

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.

@knowledgeboy6137 4 жыл бұрын

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

@dana-ff9cf 10 ай бұрын

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

@curtpiazza1688 3 жыл бұрын

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

@user-bt4vm3jl2j Жыл бұрын

Excelente explicación, usted explica perfecto amigo...

@mr.madlad1210 4 жыл бұрын

Thank you for this.

@Elitea20 3 жыл бұрын

Professor Dave really knows everything

@fabianousim6716 2 жыл бұрын

just realized the same thing lmao

@crismiranda9188 4 жыл бұрын

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

@dwarf2125 Жыл бұрын

U made it so easy bro appreciate it

@jasonb.6623 Жыл бұрын

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

@mosshead_vinsmoke 3 ай бұрын

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 2 ай бұрын

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

@potatomudkip 3 жыл бұрын

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

@janmarcusteves725 4 ай бұрын

Bro this did clarify everything, tysm

@AceOfHearts001 Жыл бұрын

Brilliant, thank you

@khloetran69 4 жыл бұрын

Awesome video thanks a lot

@franzjarvybaconawa1082 10 ай бұрын

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

@jds189 4 жыл бұрын

brain hurty

@kevinkelly6492 3 жыл бұрын

lmao same

@IbrahimAkar-pi1fu 4 ай бұрын

this is the best class i've seen.

@mechikaboombayah4960 6 жыл бұрын

You explain so nicely!!!!! #RespectToProfessorDave #FromIndia

@Minespidur 5 жыл бұрын

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

@ProfessorDaveExplains 5 жыл бұрын

i did that! keep going through the series.

@JesusMartinez-zu3xl 2 жыл бұрын

I actually understand this! thank you

@freyappari 5 ай бұрын

Thank you brotherrrr

@curtpiazza1688 2 жыл бұрын

Wow! I wish I had you for calc!

@dilanurkok5316 3 жыл бұрын

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

@RadoHudran 2 жыл бұрын

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 Жыл бұрын

Not a correction. Just another way of doing it.

@starrk_sama 3 ай бұрын

I hate engineering lmao

@user-hn1sw6nf6s 4 жыл бұрын

Thanks 🙏🏻 .

@andrewgarcia9976 Жыл бұрын

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 Жыл бұрын

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

@SAL404w 5 ай бұрын

This an insanely good way to teach a hard subject, G professor

@manpierre571 Жыл бұрын

you are the master professor....I have to pay the fees for sure 😆

@user-lg2dx6zb9j 3 ай бұрын

this made the most confusing thing I've ever done slightly less confusing, every time you help

@adityaadit2004 4 жыл бұрын

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

@Thee_Contented 2 жыл бұрын

Very educational indeed

@danielalexanderreyespineda1131 5 жыл бұрын

u r fantastic

@aryanchauhan113 11 ай бұрын

THNKS REALLY HELPFULLLLL

@zzzzzzzjsjyue2175 2 жыл бұрын

best vid ive seen on this

@yerushaleyim3655 5 жыл бұрын

Thank u..

@naseralhamwai7627 3 жыл бұрын

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

@pluto4301 3 жыл бұрын

This professor saves my grade every time

@EvilSandwich 2 жыл бұрын

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?

@BobbyC-be9vy 2 жыл бұрын

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

@NewWesternFront Жыл бұрын

why

@ijazulhaq6078 4 жыл бұрын

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

@platysmemes7663 Жыл бұрын

thanks!!

@yamkelabalisa7330 5 жыл бұрын

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

@kashifhussains2951 3 жыл бұрын

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

@unusualfrog779 3 жыл бұрын

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

@nirupamam2814 4 жыл бұрын

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

@jkgan4952 Жыл бұрын

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!

@elamvaluthis7268 Жыл бұрын

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

@thomascarter8833 10 ай бұрын

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

@Salamanca-joro 4 ай бұрын

Dude no way you made everthing this simple

@Jake-uo3ne 2 ай бұрын

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

@shaheenbean Жыл бұрын

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?

@krishgoogol8653 2 жыл бұрын

Thanku so much sir🙏🙏

@silentintegrals9104 2 жыл бұрын

totally agree!

@siausoonhong6905 2 жыл бұрын

Best Ever

@vix2740 Жыл бұрын

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

@sondosnagib6808 3 жыл бұрын

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

@dessy8634 5 жыл бұрын

I am from Ghana you are the matrix of calculus

@marcushendriksen8415 5 жыл бұрын

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

@ProfessorDaveExplains 5 жыл бұрын

pretty please tell your friends about the channel!

@marcushendriksen8415 5 жыл бұрын

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

@rabia8877 4 жыл бұрын

Weldon sir

@joshuareyes1560 3 жыл бұрын

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.

@TheSkilledTroll10 4 жыл бұрын

Do you have integration by partial fractions

@Localpref416 5 ай бұрын

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 5 ай бұрын

You factor out a^2

@topapo3661 5 ай бұрын

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

@SodiumOverdose 5 ай бұрын

thank u goat

@letslearnmathematics5432 2 жыл бұрын

Can't use power rule?

@user-jz8kn6tl6i Ай бұрын

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

@AV4Life Ай бұрын

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

@user-yg97f5hfvh 4 жыл бұрын

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

@neo8352 5 жыл бұрын

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

@RazorM97 5 жыл бұрын

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

@Divine_Discoveries Жыл бұрын

toughest video till now, but i completed it

@CoderSV3 Жыл бұрын

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

@topapo3661 5 ай бұрын

doing u substitution inside of trig substitution

@aashsyed1277 3 жыл бұрын

Ill give you 1 million dollars for this. Thanks.

@beegil911 4 жыл бұрын

man this thing is hard

@beegil911 4 жыл бұрын

its like nightmare

@maimomirabel2685 2 жыл бұрын

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