❖ Trigonometric Substitution ❖
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- Trigonometric Substitution in Calculus: A Step-by-Step Example
In this video, I explore a basic example of trigonometric substitution in calculus. Trigonometric substitution is a powerful technique used to simplify integrals, but it requires different substitutions based on the expression involved.
🔍 What You’ll Learn:
The concept of trigonometric substitution and when to use it.
Different types of substitutions for various expressions.
How to label the right triangle from our initial substitution and its importance.
A complete example demonstrating the substitution process and integration.
Tips for handling tricky integrals that may require additional techniques after substitution.
This tutorial is perfect for students looking to deepen their understanding of integration techniques in calculus. By the end of this video, you'll be equipped to tackle trigonometric substitution problems with confidence.
Don’t forget to like, subscribe, and hit the notification bell for more math tutorials and calculus strategies!
#TrigonometricSubstitution #Calculus #MathTutorial #Integration #EducationalVideo #MathHelp #ProblemSolving #RightTriangle #IntegrationTechniques #AdvancedCalculus
I just love how the majority of the examples you do, you do them in permanent marker.....no mistakes, such a beast.
misterkmo
May be sir just redo everything when he got a slight mistake.
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I can't imagine how many all-nighters I pulled just to watch his videos and understand everything so clearly. It makes calculus so easy cuz of him. :D By the way it's 2:59am RN and still seating on my chair listening to this guy. Thanks for saving my grades!
How many people made this far(Calculus II)? We are absolutely minority.
+SMEXY! Nah, man. You're in a minority once you finish diff eqs. and linear algebra.
+Victoria Havlicek Abstract Algebra
Marcus Hines My point is that you're in a minority once you finish courses that emphasize computation.
+SMEXY! i took calc 1, calc 2, calc 3 and diff eq, then transfered to a diff school, but couldnt get calc 2 to transfer (grade below a c), so im taking it again..one would think its not as hard...but nope..here i am watching these videos...again, and thank you +patrickJMT
I did up to Linear Algebra and ODE
Just wanted to say thank you for doing the Lord's work
+Rob Miles jesus, math teacher extraordinaire
+Rob Miles thanks for the laugh
Wow, i actually get it now. My professor skipped like 10 million steps during lecture
They have a habit of doing that
Yea. So did mine
did u graduate yet
@@whatshouldwecallyou9503 probably
Lol they do that too often
Man I got a Calc 2 exam tomorrow and I think you might have just saved my life!!!
did he save your life
Are you still alive? I got a calc 2 midterm tomorrow aswell
No response. Guess he didn't make it...
Joe Billy they tend to throw curve balls on exams. He should have taken this basic explanation video and applied it to more challenging problems before his exam!
That moment when patrick JMT drops a sick beat while doing calculus. (12:09)
This made me laugh a little more than it should have.
This is the most funny thing I heard today, youre awesome
hahahahaha
hahhaha DJ JMT!
4 Years later, I'm still laughing at this. I love the internet!
lol got an ad before that said "are you sick of youtube video from 2006"...why no, no im not. these video's are timeless and absolutely perfect. thanks for helping everyone pass calc 2 for free, keep on keeping on.
how do u hear video? mine wont play audio? :x
It's 1:01 AM right now and I got what I needed from you for my midterm in a 9 hours. Subscribed since 2013 and still going, thanks Patrick.
So I'm from South Africa and I'm also doing calculus. Since watching your videos after my first test till now, my marks have improved by almost 40%. I am writing a test again this week so I just bought your book (yikes to the Rand/Dollar ratio), but thank you for the great videos and all the help!
Really Patrick, you are a blessing, I'm a 65 year old composer who decided to learn calculus; I followed the full 18.01 at MIT and got lost: But with you it is pure poetry a beatiful game and your pedagogy is EXCELLENT, I know I am an emiritus teacher at university of Montreal (music). Thans a thousand times. Michel
You're such a good teacher that your videos don't even require sound and I understand them
@JohnSmith3870 glad to help! and what do you mean: if they ever get taken down with the whole censorship thing...? they are my videos, i keep them here with the help of youtube/google. :)
My Calc 2 teacher only confuses me more. I really appreciate all the examples. It helps so much with my homework and makes me like math! You should be a college professor if you are not already since you seem to have a gift in explaining complex things.
I ve watched his video as soon as I `ve had too much trouble with Math. He helped me a lot and he `s better than my teachers ever! Thank you for sharing this awesome video!
You're the man. You should have seen the looks on my calc classes' faces when my teacher (who speaks little english) introduced this topic after we were still reeling from trig integrals. Priceless lol, but as always I come to your videos and understand everything. Truly thanks.
As someone who stupidly decided to take Calc 2 online because he knew he'd be working nights and days (on different days each). You have saved my grades. Trying to read my professors notes he posts online, or follow his messed up organizational system is beyond impossible. I'd rather try to do calc 2, while still in middle school then try to follow some of his trains of thought. Whenever I get stuck I come to your videos. (Which has been a lot, especially for trig integrals). Only thing I wish you did more videos on, (maybe it's because it baffles me a bit) is when using washer and shell, I just would have liked more examples. That's it otherwise you are awesome!
Thank you very much ..... U just saved me from screwing up in exams ..... And now I m 100% confident that I can skip my calculus classes and Patrick will save me XD
I'm a student from Malaysia and your videos had been extremely helpful . Thank you so much !
@geekgal1000 ya, not everything is on the website ( but most of it should be!)
Needed this to refresh my memory. Taking differential equations next semester and need to re learn integration techniques.
i watch your videos for quick refreshers every time I have to tutor someone. I appreciate your videos greatly
What I meant is, the steps just going through the problem is a lot. Thanks for your tutorial.
YOU ARE A GENIUS.
Going from theta to x is what used to throw me off. I didn't know where to get all my substitution from. One of my friends tried explaining the triangle thing but he used it from the start and that only worked sometimes. D:
So now I know:
x to theta: memorize the rules/substitutions
theta to x: draw the triangle.
Thank you!! :D
The hero that nobody asked for but everyone needed.
definitely struggling with this is, i havent remembered/used SOH CAH TOA in years. all the things ive forgotten are making calc 2 unbearable. thanks for the refresher. every bit helps
Final time. Needed a refresher on these, thanks Patrick! Gonna pass with an A unless I get like a 55% on the final thanks to you ☺️
I got it all up to where you have to put theta back into x before watching this video. Now I understand! thanks!
@zloyhimik typically people do not want to see it this way; using the right triangle produces a much more simple equation
Usually the radical you get by doing the triangle at the end won't be the same if the problem starts you out with a quadratic equation in the square root where you need to complete the square to use substitution.
you responded! i'm starstruck dude. We all appreciate the effort it took to do this!
@cgsuperpanda1 no problem, happy to help : )
I have a quiz tomorrow on this hoping it will help.... I watch your other videos and UR DEF THE BEST TEACHER/WEBSITE ONLINE!! Id say better than KHAN ACADEMY! :D Thanks for putting this up you're seriously the best!
Holy hell.. this type of problem has it all.. a true test of one's mathematical prowess.
I could never understand my Calc BC class without your help, thank you soo much!
This guy is my favorite math tutor lol. Well done, great video.
there is a ton of stuff missing from my website. it is a nightmare to keep updated
@42marthacu glad you like them : )
lol finally clarified what i was confused about in the last step…THANK YOU !
I've always wanted to integrate a cheese burger, who wouldn't. Not sure if u-sub, parts or trig sub would be appropriate.
Zafar Adel I feel like you can integrate many by inspection.
it is not from beyond; it is from my small little room in austin texas!
Wow. How convenient. I was just getting ready for a trig sub lab, and this video helped me out big time. You are basically my calc professor
WOW that this video was so helpful. I missed lecture for this topic and after watching the video don't feel behind at all! You ROCK! :)
Thank you! for some reason I could not wrap my head around this. but you cleared it up!
Awesome video, prof never told us that little hint for the missing angle usually being in the original question.
@Puggalug yep, this is true!
Hey patrick! You da man! Just so you know, I don't think this video appears on your website and I couldn't find it on your channel until I searched for it. I started on ex 2 and I was confused but not after this one so you may want to make a note on the video or something so people don't get confused idk... Thanks though! My friend and I don't go to lecture any more because we just watch your videos!
Thank you so much!! Test tomorrow. hope i do well. I actually do have a pretty good teacher, but unfortunately this was the one day of lesson that i was gone. I'm feeling much more confident in this now :D
@patrickJMT more like, Khan and Patrick are gonna rule the internet with educational videos!
thank you so much maan you are a life saver :)
i have a little comment 4 u :
if you want to find the angle, there is an easier way just use the inverse of theta
again thank you sooo much
@patrickJMT
Thanks for confirming. I love your videos and I am actually a Calculus tutor so it's nice to receive that sort of confirmation from a math person such as yourself.
Would you consider making a follow-up video showing this same question solved using u-substitution, and thereby illustrating the difference between using u-substitution and trig-substitution?
Is there a "magic formula" to know when you can use the u substitution and when you have to do it the trig way?
Also Thank you for all your helpful videos!!
You should definitely try the triangle method!
Professor Patty comin' through once again.
Thank you Patric, I learnt a lot from your videos (especially calculus)
He cubed 4 and then multiplied by the other 4 (from 4cos(theta) when plugging in d(theta) for dx). And (sin(theta))^3 == sin^3(theta)
When u have cos^2x or sin^2x to integrate, how do you know whether to use sin^2x+cos^2x=1 or the sin^2x=1/2(1-cos2x)??
Hi do u do 1 on1 online tutorial?...I am ready to sign up for the next 5 weeks. You are amazing man!
At around 9 minutes, I noticed that in your u sub you made the one into a cos theta. When you derive the step you see at 9:13, you don't get the integral because cosine isn't a x. It derives to -sin x. Am I just confused?
@jsweat2011 this is how i describe it to people
Saved my life again!
Thank You So much for doing these videos.
@daemonpacman must be the calm soothing voice that lets you concentrate better^^
This is why I don't like to go to school anymore. I mean in it a good way. I really don't think schools nowadays are different from intelligent videos like this one. Thanks
Is there any way to donate to keep this free? Very helpful
Thanks for video and explaning everything part by part
man great timing. i just learned this lesson today. love you man
@82windows82 that's the best way, since you can "cut" the terms after...
are there any videos on doing these trig integrals with hyperbolic trig functions?
when I solve this problem using u-substitution, the answer I get is:
-6 sqrt(16-x^2) + C
Is that the same answer you got using trig sub, only simplified more? Or did I just do the problem wrong? If it is the same answer, how do I simplify your answer to reflect mine? Any help would be awesome because I am a little lost. Thank you.
12:11 scared the crap out a me!
please explain why we could not take u=sin(theta) there at (7:24)..why we taken there u=cos(theta) ??
please explain
In my understanding, it's easier to say u=cos(theta), as du will then equal -sin(theta), which will get rid of the sin(theta) d(theta) once you substitute.
well .. currently your videos are saving my life , thanks alot bro :)
Great video and clear instructions! Thank you!
At 6:16
4³.sin³∅ = x³
And putting the value of dØ , we can do it easily
My man! I was up late last night trying to figure this out and I'll pass thanks to you!
Bro, do you have examples for "half-angle substitution" and "reciprocal substitution"?
@UnicornOnTheCob16 nah, more like a good TA
Hi, great explanation, but the triangle drawing wasn't necessary. Writing
x=4sinT=4*sqrt(1-(cosT)^2)
and Isolating cosT would have been shorter.
these videos are THE BEST
I was confused at first by the asin, atan, and asec notations. I thought they were arcsines or sin^-1s. Other than that, this video is so helpful it probably just boosted my midterm grade by at least a letter.
@thanu31 i think there is room on the internet for both : ) he makes good stuff, for sure
Dude you should come teach at Morgan State in Baltimore, MD!
god when you blew into the mic. at 11:42 i jumped haha scared the shit out of me
Patrick is my real teacher.
Just another way to remember the right angled thingy..
"SOME PEOPLE HAVE CURLY BLACK HAIR TO POSSESS BEAUTY"
sin=perpendicular/height;
cos=base/hypotenuse;
tan=perpendicular/base;
Thank you it is very useful , Use noise reduction mic for better sound
every time i finish ur videos i hav that "OHHHH-" moment :>
thankYou!! this explanation really helped me understand what is hapening.
thanks for this video!! it helped a lot! you explained it way way better than my college professor, wish that u were my professor instead of her! lol
Thank you so much for posting this, all your hard work is much appreciated!
I will pray for you every single day, until im done with my finals
Moutaz Anis ادعيلي معاك
SOH = sin = opposite/hypotenuse
CAH = cos = adjacent/hypotenuse
TOA = tan = opposite/adjacent
Game Changer
CHO = csc = hypotenuse/opposite
SHA= sec = hypotenuse/adjacent
CAO= cot = adjacent/opposite
The chief
You are the best person ever.
Thanks for this video it really help me a lot.
You the real MVP
@Mo0dshift3r it is not just you : )
It’s really difficult and scary at first but when I started solving it gets easier the more i do it
my gratitude to you
why we didn't take the square root from the beginning at the denominator and take 4 common factor instead of 16 and let it
(@ equal to 4(1-sin
and then let( 1-sin@) equal to( cos@) instead of( cos@ )squared
is it possible
you are very welcome :)