Trigonometric Substitution - Example 2
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- čas přidán 18. 09. 2008
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Trigonometric Substitution
A complete example integrating an indefinite integral using a trigonometric substitution involving tangent.
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Dude you explain 1million times better than my professor
as I always say Patrick you are the best person in the whole world
Patrick - You, in conjunction with Salmon Khan are the reason that I feel confident going into an engineering career, switching over from music. I always loved science/math, but having a rough time at home in middle/high school prevented me from concentrating. You allowed me to test out of Calc A without even taking the class. These videos are so empowering. It's really transformed my future in a way you can't imagine. Thanks so much, and I hope you understand what an impact you have on people!
Not a topic goes by in math that I don't understand, no matter how tough thanks to you! I am and aengineering major and currently taking calc 2 and linear algebra; we just finished this in calc 2 and are started parametric equations. You are more helpfulrthan any professor I have ever had. Thank you for helping me to understand this difficult material!
@Wilson1989SWE nope, i did not even graduate high school. mainly, i just make this stuff up as i go along, but i say it in a convincing tone
You sum up in 10 minute videos what my college professors fail to teach in weekly sessions... freaking awesome, thank you.
I spent almost an hour trying to do these problems on my own, I looked at your first video on the subject and I got the problem in this one right after. Thanks so much!
Patrick you're freaking awesome. Missed my math class last week sleeping in and I don't even have to look at my professor's notes online cause you already covered this topic. I feel like I won't ever have to show up in class, I'll just have to look up the topic in your channel and take notes watching your videos. thank you.
@patrickJMT and by calc 2, i assume you will just start integration... but i am not sure about that now, given the material in this video!
@brawl313 i would make sure you remember the basics: how to do a variety of limits, derivatives, basic trig stuff (identities and values and such), and make sure your algebra is ok (basic graphs, solving equations, etc). if you feel up to speed on all of that, you can always read ahead and get exposed to it before next semester; at that point, you will be brushing up to some extent, instead of seeing it for the first time.
@silverback0156 i posted it on google video long ago, but it never made it here
You are the translator to my professors's gibberish. Thank you, O Great One.
You have no idea how much your videos help me, thank you so much!! keep it up!
I should just start homeschooling calculus to your videos :D
And I haven't even LEARNED Trig substitutions yet! Yet I still understand you perfectly! I go to your videos to get ahead.
Superb job!
I have a quiz on this in about an hour! I was out on a date last night, so I didn't study and now here I am getting a crash course on this WOOOOOO lol. I've been recommending PatrickJMT and Khanacademy in every math class I've been in, since I discovered you guys.
Wow. You are really helping me understand Cal 2 WAY more in under 10 minutes than I do in 2 hours of my professor's class. I now feel more confident in college calculus thanks to you. If I pass this class this semester, it'll be because of you. Thank you so much!!!
omg i finally get it! i might actually be able to pass my test today!
thank you so much patrick! i don't know what i would do without you and your amazing videos
Man. I love with all my heart. You have made everything so clear.
@Wilson1989SWE i have a master's degree in math, worked on a phd before i realized it was not for me, taught at a top 20 school and a couple of other places, so i am not totally clueless at least (i think)
I have a test in less than an hour, and an F in the class. This video is helping me so much. Thanks. *thumbs up*
Did you pass the class? haha Right not im in that exact same boat FML
Horrible.... i hella failed the test
I need a miracle im extremely lost in my calc 2
pray for me idk if dat works
I'm great to see that all of your tutorials, it's very helpful. Keep on going more and more.
Thank a lot.
@sp22kn4 i can not remember if i have a video with this or not...
Thanks Patrick. This is helping me greatly to catch up in Calc 2. By far the most complex math course I've taken yet. Up there with Discrete Math.
this coming from someone named 'halo prodigy' - i bet you get all the babes
Trig substitutions were one of the most difficult to grasp aspects of my calc 2 class. Even the student math tutor, who had taken through diff eq had difficulty explaining them.
Patrick you've saved me time and time again... you're a miracle worker.
Wow, I really think you just saved me grade. It sort of feels like my life. I was sure I was going to fail my exam tomorrow, but the I found you! Thank you SO much!!!
@lilslush06 ha, happy to help : )
I'm literally laughed so hard at that XD. Patrick, my dear youtube friend, it is unbelievable that you can make such helpful videos. You make me enjoy math, particularly Calculus. Thank you
thank you so much for doing these videos I have a quiz tommorow and I was scared I didn't know how to do trigonometric substitutions really well and you cleared that up for me. Also you explain really well. I guess professors can't explain well because there's a time limit on what they can teach so I'm glad you're doing these videos.
Patrick!!! Greetings from Saudi Students in the US!!!!.. you really helped us passing tests ;)
wow this was sooo helpful i've been trying to find a example like this all the one :D
I love your videos they're so helpful!! Thank you
-student cramming for her midterm
MY PROFS SHOULD STAY HOME AND YOU SHOULD TEACH ME! THANKS FOR SAVİNG MY LIFE!!
This is so helpful...
Thank you so much for making these, i would be completely lost if it wasn't for these videos
@a02sweetdream i try : )
I just wanted to say thank you so much for posting these great videos. My professor is a great guy and very smart, but he does not know how to teach. You are awesome! Keep it up!!!
CZcams is made for patrickJMT!
i actually hate how your left-handed. But dammit, your really good at explaining things better my calc142 prof.
Owen556 calc142??
He meant Math 142, which is Calc 2
this 7 min video was more valuable than 2 hrs of my professor's lecture
THANK YOU SO MUCH! You're an awesome teacher. God Bless You! ^-^ You make it so easy to understand.
Wow I just read the comments and see that you truly are making an impact in the world we live in today, indirectly. You are the man!!
love these videos!
thanks for sharing.....you helped us in our integral calculus
@pwnagenation1 glad i was able to help!
@saweeetx you know it is
it's calculus...in HD!
Thanks for your videos Patrick, they are insanely helpful
I space out at lectures so i understand my math now because of you
thanks a lot ! this video really helped
thanks for the kind words :) it is a great time we live in i think!
thanx sir, you are amazing at explaining the subject. Keep up the good work and thank you again
What a great tutor!.. finally got it
Great explanation! Let's hope that there's nothing too crazy in my exam tomorrow...
The explanation is very very good thanks
I'm looking at this right before an exam. I Finally understand!!!!
dude I have a similiar background as I just started engineering school. I keep playing music these days and these videos are really saving me time as well.
Lifesaver... THANK YOU!
in just two words, love you
thank you so much!i've got a calculus exam tomorrow and i was having a panic attack coz i didnt know how to solve a trigonometric substitution but this video is like a miracle gift from the sky. :D
you teach exactly like my calculus teacher! and that's a good thing!
@patrickJMT: Excuse me Patrick. I have one question about this problem. Where do you get the tan theta from? And thanks for the legendary videos! They are extremely helpful!
tnx bro this video help me alot keep it up.
i cant say this enough, you're awesome!!!!! how is it that i get what you teach within the 15 minutes vs. my teacher who talks for hours..
thanks ;)
i like both
OMG!! I love you soo much :D This vid is a big help.
knowing the values of x in terms of theta, you can equate the make the denominator 9x^2 + 4 equal to 2^2 tan^2 theta + 4 and simplifying, 4tan^2 + 4 theta will be equal to 4 sec^2 theta using the identity (tan^2 theta + 1 = sec^2 theta)
thank you for the video patrick.
question; how do you know when to use inverse substitution or normal substitution like this video? i'm confused:(
thank you! thank you! thank you!
This is good review for the my finals. Thanks, I feel like I should be paying for this
you are a lifesaver, patrick.
HAVE MY BABIES
thank you soooo much!
Awesome bro!
@sp22kn4 Do you mean change the bounds of the integral? It's simple. When you make a u-sub. you can take your original upper and lower bounds and put them into your u-sub equation as x-values. So if you have a interval of [1,2]: if x=1 then u would be =? and if x=2 then u would be equal to? replace the bounds with your new values. This way you have the values of what you substituted in for u.
You are awesome...Thanks!
best explanation there is
thanks professor
Thank you!!!
how would you know to use this instead of sinh^-1(u/a) because since the stuff in the radical is being added can't you flip it around so that it will be (dx/sqrt(4+9x^2) to make it look like d/dx of sinh^-1 x?
So I left BBC Sherlock's theme melody play in the background while watching this... The level of epicness is OVER 9000 !!!
At 5:40, Is it reasonable to use theta=arctan(3x/2) ? I was thinking it would look too complicated to have arctan inside of sec and tan, but is it wrong?
I love your videos, you explain so well that I, a junior in high school understands it perfectly. I have been teaching myself calculus and your videos come in handy, I thank you very much. Keep up the outstanding work.
You can make the right triangle at the start of your integral and substitute EVERYTHING in. It's so much easier.
How do you mean?
at 4:40, when you wrote ln of sec + tan, is there a reason its in between those lines instead of parentheses? its not absolute value is it?
Thankyou! Thankyou! Thankyou!
lol i doubt you will read this but i would like to thank you so much for your videos this one problem has taught me more than my teacher in 2 hours of lecture
this has to be the hardest part of calculus 2 sooo many things to do!
Hector Borges just finished my 2nd week of calc 2 - is this really the hardest part of the class? If so, this class is going to be a breeze. Somehow I don’t believe you though 🤣
you are awesome !!
Thanks! :)
Patrick quick question, would this be correct also?
(1/3)In( whatever / 2 ) + C
(1/3)In( whatever ) - In(2) + C
(1/3)In( whatever ) +C
My gpa greatly thanks you
agreed.
@spychic101 these are supplements. and there is not much to think about in this case; it gets rid of the radical via the identity. nothing deep or magical.
you make calculus so much easier
Thank you.
Anybody trying this out should draw your triangles first! If you have a integral with a fraction in it that includes a radical remember that if the sign inside of the radical is "+" then you have your hypotenuse. If the sign inside of the radical is "-" then you have one of your sides.
you are amazing.
okay could you possibly do an example where you end up with and answer for the integral in terms of theta where one of the parts of the equation is something like 2(sin2(theta)) and go over how to plug back in to get that back into terms of x? that is really confusing me right now
after watching your videos, i can answer our quizzes in less than 5 minutes! hahahaha
thank you bro! God bless!
you make this look so easyy....:)
Dude wait... don't these things integrate to inverse trig functions? Are they numerically equivalent for definite integrals? Do you use the ln form as a workaround for domain restrictions or something? You could have just solved for theta algebraically and gotten an inverse hyperbolic sine function right? I'm working on some of these problems right now and I don't see the point of doing it this way vs. looking it up on a table.