❖ Trigonometric Substitution - Example 2 ❖

[@scottydscottd]

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!

[@arielesilvatroche5473]

Dude you explain 1million times better than my professor

[@hassonal-mu2524]

as I always say Patrick you are the best person in the whole world

[@Mustang5Speed]

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!

[@theGameQueen]

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!

[@holmes9405]

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.

[@LeadIntoZer0]

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.

[@darrianellison4497]

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!!!

[@justinschuster3794]

You sum up in 10 minute videos what my college professors fail to teach in weekly sessions... freaking awesome, thank you.

[@catherineouellette7088]

You have no idea how much your videos help me, thank you so much!! keep it up!

[@tenken1337]

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

[@jemelmonger]

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*

[@mustangbee17]

Did you pass the class? haha Right not im in that exact same boat FML

[@mustangbee17]

Horrible.... i hella failed the test

[@mustangbee17]

I need a miracle im extremely lost in my calc 2

[@neil9151]

pray for me idk if dat works

[@joslinnick]

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.

[@MoreKevinLiang]

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!

[@saharasmith4274]

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!!!

[@WarriorsFan]

Patrick you've saved me time and time again... you're a miracle worker.

[@patrickjmt]

@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)

[@conman607]

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!!

[@silentcod3r]

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.

[@shikori7]

Man. I love with all my heart. You have made everything so clear.

[@patrickjmt]

@pwnagenation1 glad i was able to help!

[@YawningBoy]

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.

[@patrickjmt]

i like both

[@patrickjmt]

@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

[@mishnareemincey]

You are the translator to my professors's gibberish. Thank you, O Great One.

[@patrickjmt]

@saweeetx you know it is

[@patrickjmt]

@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.

[@AlfnnanVip]

Patrick!!! Greetings from Saudi Students in the US!!!!.. you really helped us passing tests ;)

[@aom9010]

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

[@patrickjmt]

thanks for the kind words :) it is a great time we live in i think!

[@patrickjmt]

agreed.

[@adisornee44]

I'm great to see that all of your tutorials, it's very helpful. Keep on going more and more. Thank a lot.

[@Tias98]

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!!!

[@xXMcBeanXx]

it's calculus...in HD! Thanks for your videos Patrick, they are insanely helpful

[@raysonkong]

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.

[@nanyoo2009]

I love your videos they're so helpful!! Thank you -student cramming for her midterm

[@ermitanyongmahileg]

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)

[@patrickjmt]

this coming from someone named 'halo prodigy' - i bet you get all the babes

[@conman607]

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

[@chocochris93]

I'm looking at this right before an exam. I Finally understand!!!!

[@kigomakid]

This is so helpful... Thank you so much for making these, i would be completely lost if it wasn't for these videos

[@RainbowPaint]

wow this was sooo helpful i've been trying to find a example like this all the one :D

[@patrickjmt]

@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!

[@chocochris93]

I space out at lectures so i understand my math now because of you

[@padzman91]

KZbin is made for patrickJMT!

[@princeamethyst]

thanks for sharing.....you helped us in our integral calculus

[@nombusokhumalo3138]

What a great tutor!.. finally got it

[@patrickjmt]

@lilslush06 ha, happy to help : )

[@moonbathing2146]

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..

[@patrickjmt]

thanks ;)

[@persondude911]

this 7 min video was more valuable than 2 hrs of my professor's lecture

[@kyleairforce]

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.

[@juanbecerra5073]

Great explanation! Let's hope that there's nothing too crazy in my exam tomorrow...

[@hibahabosha1732]

The explanation is very very good thanks

[@monicamoomo]

Thanks! :)

[@wuba556]

i actually hate how your left-handed. But dammit, your really good at explaining things better my calc142 prof.

[@justdusty9697]

Owen556 calc142??

[@xInsaneJuggernautx]

He meant Math 142, which is Calc 2

[@Karim-ud9kl]

in just two words, love you

[@missingtheory]

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.

[@willeseswils]

@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.

[@GigiAlfonso]

MY PROFS SHOULD STAY HOME AND YOU SHOULD TEACH ME! THANKS FOR SAVİNG MY LIFE!!

[@mrCLICKman]

you teach exactly like my calculus teacher! and that's a good thing!

[@redioxrediox747]

thanx sir, you are amazing at explaining the subject. Keep up the good work and thank you again

[@aroojqureshi8012]

THANK YOU SO MUCH! You're an awesome teacher. God Bless You! ^-^ You make it so easy to understand.

[@xiaolintraditional90]

you make calculus so much easier

[@patrickjmt]

@sp22kn4 i can not remember if i have a video with this or not...

[@Caphalem]

So I left BBC Sherlock's theme melody play in the background while watching this... The level of epicness is OVER 9000 !!!

[@patrickjmt]

@badluckarri LEFTY POWER!!

[@leiru01]

This is good review for the my finals. Thanks, I feel like I should be paying for this

[@h2dkbond]

thanks a lot ! this video really helped

[@mbusomabuza7273]

best explanation there is

[@dancedynodance]

Lifesaver... THANK YOU!

[@pwnagenation1]

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

[@Binkers9]

love these videos!

[@Zellean]

this has to be the hardest part of calculus 2 sooo many things to do!

[@dwwwwwwwwwwwwwwwwwwwwwww]

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 🤣

[@patrickjmt]

@silverback0156 i posted it on google video long ago, but it never made it here

[@blendder35]

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

[@patrickjmt]

@a02sweetdream i try : )

[@vd853]

it should be call calc^2, u can get an A in calc1 and easily get an F in calc2, anyways this vid help me figure out the converting back part thx

[@shaners24]

thank you! thank you! thank you!

[@MrMidnightSpecialist]

@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!

[@ned272]

You can make the right triangle at the start of your integral and substitute EVERYTHING in. It's so much easier.

[@thebgEntertainment1]

How do you mean?

[@patrickjmt]

dont be a slacker. at least, not completely! todays slackers turn into 40 year old pizza delivery people

[@EngrGidz]

tnx bro this video help me alot keep it up.

[@Onigirli]

you are a lifesaver, patrick. HAVE MY BABIES

[@sigalig]

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

[@MultiMoe91]

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:(

[@thizIzNyancat]

OMG!! I love you soo much :D This vid is a big help.

[@solariaeuropa3669]

Thankyou! Thankyou! Thankyou!

[@unknown4091]

thanks professor

[@dansdumpsite]

why is there 2 dx?? thanks tho. your videos help me a lot :)

[@yasmine8744]

My gpa greatly thanks you

[@Fingolfin1394]

How does the 2 cancel out at 3:45 ? Isn't that a 1/2? Great videos though! Incredibly helpful!

[@zwiblob]

Hey patrickJMT, I've got a question. If you use for dx/(root(9x^2 + 4)) the formula integration of du/(root (u^2 + k)) = ln( u + root(u^2 + k)) +c (this one is in my math book) you get the same answer, except the two components of ln are not times 1/2. I doubt the formula from my math book is wrong, but I evenly doubt you made a mistake, I didn't find one anyways, but one of these has to be wrong.. :/

[@ssm1187]

You are awesome...Thanks!

[@addman2k7]

@sp22kn4 When it comes to making a substitution, i.e changing x to u, the limits on the integral are valid for f(x), not f(u). You are perfectly right to re-substitute to get your final answer in terms of x without changing the limit. If you wish to calculate the integration limits you need to directly substitute the limits into the u equation. So, if you say had u=sinx, you would put the a and b values for x in, then replace them on the integral and use the flip trick if neccessary. Zombie259

[@123456789012573]

God bless you Mr Pat............Wais from Afghanistan Kabul

[@AlexBrunner94]

Technically, could do a triangle to not have to deal with a messy integral instead?

[@emilygraham7774]

Thank you so so much!!! I don't understand my profs accent and I have a test in three days!!!

[@AndyU96]

+Emily Graham IF-f many others are having the same problem understanding the professor, then talk to him directly about it, or talk to the uni and have him changed, uni is for education, and a lecture is to teach, and to teach means to make someone know (I think). If the teacher cannot be understood, then he shouldn't be there to teach in the first place

[@traceohrt4930]

Unfortunately many colleges don't hire professors for their teaching ability but for their research. For many professors the teaching part of their job is a very small percentage of their actual work. This is why there are many "bad" professors out there. The college might not really care so much about the teaching aspect and how well the students react to it if they have worthwhile research that gets the college grants. You just have to play the game.

[@percslushee8411]

When finding dx=2/3 sec^2(theta) d,theta can't you also write 3/2 dx = sec^2(theta) d,theta? Then you would bring this out front of the integral and would have 3/2 out front instead of 2/3? I know I'm wrong but I don't understand why you cant write 3/2 dx = sec^2(theta) d,theta

[@ErniesLament]

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.

[@a02sweetdream]

you are amazing.