Trigonometric Substitution - Example 1

[Mkivfan28]

Why can't you be my Cal 2 teacher? Thank you very much

[Gixxiemoto]

i never understood the right triangle part until your video,thank you!

[Melhimri]

Is there any way to donate to keep this free? Very helpful

[barbarax30]

thank you sooooooo much!!!! i had nooo idea how to figure out where the units go on the triangle... my professor always did it as one of the first steps and i was like huh? but doing it later in the problem like you did is sooo much easier to understand! thanks bunches

[patrickJMT]

@barbarax30 good luck!

[sunnysideupt]

You're my hero!!!! Friends recommended you to me, and I've recommended you to friends. I don't know a math student who hasn't heard of you! THANKS PATRICK!

[patrickJMT]

@sunnysideup no problem, happy to help :)

[killerABcs]

I got it all up to where you have to put theta back into x before watching this video. Now I understand! thanks!

[Angelgrrl04]

So we basically just need whatever is under the square root, somewhere back into our ending result right?

Because my professor said the answer should be the original, which I noticed it obviously wasn't the exact same.

[serioushamster]

And I thoughtSOH CAH TOA wa my memonic

[AndrewMon2008]

this is really helpful, thanks! much appreciated

[Jakobe565]

thank you for actually teaching in the vernacular instead of Mathenese like my teacher

[stlcardsfan530]

You sir, are a hero

[freakoftheyear]

You saved my life. :]

[jennygallery]

how do you manage to make everything so much easier?!?! i love you!

[yaldoyousif]

I love you :)

[MyNamesCamila]

I think I love you... Thank you so much.

[23SuS23]

Got my mathematics degree from University of Tor...err PatrickJMT

[patrickJMT]

@23SuS23 ;)

[tsaxplaya0708]

I just want to say thank you so much for your videos. They are so helpful and in depth. I would not be able to pass my Cal 2 class without these videos! Thank god for your brains!

[sithlordkoko]

Really helped. Got lost on how to return theta to x but after viewing your video I understand it much better. Thank you!

[vanadinite01]

Like everyone else here says, thank you. very, very, much. Seriously.

[patrickJMT]

@vanadinite01 no problem, happy to help : )

[FincayraMerlin]

thank you so much...my teacher taught us by having us draw the triangle first, which I did not understand at all!

[phanelius]

This looks like fun :) , I really enjoy every video of yours. I LEARNED IT AT PratrickJMT COLLEGE =)

[patrickJMT]

@phanelius lol

[philster00700]

I love you, not like that though.

[RECxLESS]

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.

[Thunder7messiFan]

@RECxLESS Lol, that's my experience exactly. These videos Rock!!

[angelsword1000]

Seriously the best video. Thanks so much!

[patrickJMT]

@angelsword1000 you are very welcome

[Triathletep]

what is the u substitution??

[noneabove1182]

I thought you'd like to know, when you got root 16 - x squared, I was yelling at my computer screen that no, this was not possible. Thank you so much for helping me understand :D:D:D

[ziadosi]

nevermind, you explain it in a later video..thanks! :)

[ziadosi]

im trying to solve a problem that starts out like this: 1/(9+4x^2)^(3/2)

ive followed steps yet in the end it gets ugly, is there a shortcut?

[cgsuperpanda1]

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

[patrickJMT]

@cgsuperpanda1 no problem, happy to help : )

[zuzikini12]

I finally understood how to go back to x terms ...thankss :D

[bigbeard86]

too bad you dont have much of calc III (wish you did). how about some differential equations?

[thanu31]

hmm khan or partick .... tricky...

[patrickJMT]

@thanu31 i think there is room on the internet for both : ) he makes good stuff, for sure

[KillerZero259]

@patrickJMT more like, Khan and Patrick are gonna rule the internet with educational videos!

[patrickJMT]

@KillerZero259 probably khan will since gets tons of funding : ) i will sit in my little room with my $100 webcam for now

[RomanusDigitus]

Great video, but the square root of cos^2(x) is absolute value cos(x), not just cos(x), so you can't cancel out the cosines. Or can you?

[82windows82]

Is trigonometric substitution the only way to solve these 3 forms or can it be done differently?

[Marcuzzorox]

@82windows82 that's the best way, since you can "cut" the terms after...

[babycakes00777]

Your videos are soo helpful, thanks so much! I was just wondering what happened to the other 16 at around 4:40?

[calvin337]

THANK YOU

[willbitter]

You are an amazing teacher, really good paper handling skills too.

You even have ads on this thing, you must be raking in some bread.

Keep it up.

Thanks for the video

[jmmtcidc]

So far this semester, I haven't attended a single lecture for my Calc II class. I watched like 10 of your videos the night before my midterm and I aced it. You are my hero...

[patrickJMT]

@jmmtcidc ha! spread the word about the videos. that is your duty. : )

[NguyenEmpir3]

instead of memorizing the 3 rules of substitution, you can draw out a right triangle, then use sohcahtoa to solve for the squareroot, x, and dx.

just another way, in case if you forget.

[mochila467]

good vid bro pulled out 3 integrtion techniques in one vid really helpful exapmple

[LINAFATAFTA]

Thaaaaaanx

[moonzangel9]

ive been watching your vids for about two weeks now and ive been in school for about a month and a half and these VIDS actually taught me something!! thank you so much for!! i have to admit i am so awed because i never got this and yah!! now i do!! in your face to my prof. i just had to comment just to show my support for your vids, if i dont you may decide to stop posting and i dont think anyone wants that, so thank you again, you are a math genius life savior!! wish you were my teacher!! ^-^

[AvengedRocker92]

Nice Job, Really helped me out with my classwork, and found some new methods of substitution Thankx!

[blackhawkdownsnare]

That first problem you wrote, was the one I was looking at when I was like, hm, let me go see PatrickJMT on this topic. Mind-blown sir. Good job.

[patrickJMT]

@blackhawkdownsnare perfect : )

[TheNumber2Pencil546]

god when you blew into the mic. at 11:42 i jumped haha scared the shit out of me

[digit0lchica04]

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.

[patrickJMT]

@digit0lchica04 thanks for the kind words ; )

[MrSammygarcia]

@digit0lchica04 I completely agree.

[wootenwannabe]

Once again you've explained something clearly in 14 minutes that a professor couldn't explain in an hour and half of lectures. Not only do you do it in a way that's understandable, you show WHY I'm doing this, my book and professor just assumed I knew that I was factoring the 'a' out. My book doesn't even have the triangle trick. YOU ARE GOD!

[KimJong7hrill]

Wow this is what my professor did on one of the homework examples. We were all so confused on how he put trigonometric functions in place of variables and stuff. It's a testament to how bad he is. We just learned u substitution and integration by parts and then he uses this out of the blue and assumes we know what he's doing let alone that we've seen this before. It doesn't help that he's so old whenever we asked him how he put "sin" in for "t" he didn't hear us and kept on going :/

[daemonpacman]

is it weird that I talk myself through my exams in my head using your voice?

[patrickJMT]

@daemonpacman ha, whatever works for you : )

[JohnSmith3870]

@daemonpacman LMFAO this comment just made my day!!! I also wanted to say thank you SOOOO MUCH to PatrickJMT, I really don't know what I would do without these vids. If they ever get taken down with the whole censorship thing, I'm totally screwed, they help SO MUCH.

[patrickJMT]

@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. :)

[pepekong]

@daemonpacman Holy crap, I do that when I'm doing homework.

[tadoubleg]

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.

[jazzysax102391]

Beautiful, you make math into an art form. (slow clap) :)

[11m0]

How I wish u were my Calc 2 Professor...So helpful...thanks

[42marthacu]

I love you, I seriously watch all your videos

[patrickJMT]

@42marthacu glad you like them : )

[turbonetex]

patrick, your awesome bro! really helping me pass this online calc class with flyin colors i appreciate everything you do man keep it up!

[gorillabiscuits]

Patrick is my real teacher.

[powercrazy11]

Can't understand a word that my TA says so this video definitely helped, thanks patrick.

[patrickJMT]

@powercrazy11 glad it helped!

[JSasRays]

@powercrazy11 is she an asian lady?

[powercrazy11]

@JSasRays No.

[hunterwilbanks]

you have saved me multiple times

i feel like i need to pay you money

[patrickJMT]

@hunterwilbanks donation link on my website ; ) feel free to send as much as you like!

[Mo0dshift3r]

is it just me or is this guy awesome? :D

[patrickJMT]

@Mo0dshift3r it is not just you : )

[ryanmerkle5]

pardon my language but youre the fucking man!

[patrickJMT]

@ryanmerkle5 that is what my wife tells me

[FrigginSmift]

SOH CAH TOA

I always remember it as "Some Old Hippie Came A Hoppin Through Our Alley"

[jsweat2011]

@FrigginSmift "Some Old Hippie Caught Another Hippie Tripping On Acid."

[patrickJMT]

@jsweat2011 this is how i describe it to people

[ThePappas7]

i love you bro

[lncg10]

You're videos are so helpful!!!! thank you so much!

[deadlybug]

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.

[waitazechond]

I went and created this account just so that I could comment on this video and tell you thank you so much for making this so easy. I've been struggling for what seems like forever on my homework tonight, and now I finally understand all of it!

[BBQB0Y]

i love you

[18temi]

THANK YOUUUUUUUUUUUUUU!!!!!!! This video was so helpful! Best help I've received thus far from all your videos. They were helpful as well but this was HELPFUL!

[18temi]

Dude you should come teach at Morgan State in Baltimore, MD!

[sweeetburn]

DX are you ready to suck ittttttttttttttttttttt

[wavejumpinseadoo]

Using Pythagoras Theorem, couldn't you have solved for x when you had the right angled triangle? I got x=-3 or x=4. I'm not sure if it would help though...

[suny123boy1]

@wavejumpinseadoo

Stop

[MichelLongtin]

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

[daemonpacman]

I love you.

[TrueDarkness]

You're such a good teacher that your videos don't even require sound and I understand them

[neonsurge]

lol, i passed pre-calc, calc1, calc2, discrete math and diff. equations just by watching your videos. You make math look logical (y)

[Mustang5Speed]

You never fail to help me understand even the most complex problems. You are an excellent teacher. Thank yiu so much for these amazing down to earth and free explanations

[falutak]

", you should get examples from the book of Love and Rainville..

[TheCrazyLoverGuy]

is it just me? I don't see any commercials or advertisements when i'm viewing here in youtube..weird...and this vid is great..as always..

[ViolaceousDreams]

good video... :)

[yas4311]

Man ... u rock !!!!!! thx alot

[geekgal1000]

TWO commercials??? lord help us all

[JaoquinQ]

ohh i wish advertisements wouldn't interrupt halfway through, exam time is annoying enough

[mirzconsulting]

Teach online for University of Phoenix!!!!

[patrickJMT]

@mirzconsulting i did once a long time ago and it was a terrible experience

[vhunterd666]

@patrickJMT Please explain why it was a terrible experience.



[NavAujla13]

you

are

awesome

[islamicambition]

Thank you for your videos! I am just confuse as to how you are able to substitute x=asin(theta)? I mean where does that equation come from?

[patrickJMT]

@islamicambition one can substitute in whatever you want.

[Ghostlyman2]

what about sqrt(x²+a²)? Cause i see the other 3 in the vid, but this one seems a bit logic to go with them...

[Ghostlyman2]

@Ghostlyman2 ow jezus, i feel really stupid now. Offcourse sqrt(x²+a²)=sqrt(a²+x²) Nevermind my question :S :D

[geekgal1000]

ooh! this wasn't on your site! i feel like i've struck gold!

[patrickJMT]

@geekgal1000 ya, not everything is on the website ( but most of it should be!)

[StrawberryCheckers]

New videos! Thank god, you make it so much easier to understand material :)

Plus I've been looking for a video about this topic; and you're the one youtuber who explains best. Wouldn't settle for anything less

[Kevcom2]

thanks PatrickJMT! Your tutorials are much easier to digest than the material in James Stewart's Calculus Early Transcendentals!

[ramshambo2001]

Thank you so much for posting this, all your hard work is much appreciated!

[tombatable]

I think you're smarter than I am because you're left handed. :D Your videos help a lot. I've taken calc before, but i'm retaking it here in college, and out of all my classes, it's the easiest, which is bad...

[joe393987]

I pay good $ to take class at community college, and end up getting a free lesson on youtube that took about 1/5 the time of my class and about 300% clearer. I should just send you the money instead lol, since ur the one teaching me. Don't suppose u do chemistry do you? haha. You have no idea how much this has helped me, i'm telling all my friends taking calc. If you are a math teacher, your students r the luckiest in the world. Oh wait, l am your student :p lol

[bbernens]

COME TEACH AT PENN STATE!

please.

[patrickJMT]

@bbernens i have gotten a lot of requests lately to go to penn state... maybe i should give them a call.

[fldoughboy72]

NICE problem!!  love it!

[SRSM09best]

You are a lifesaver. Keep up the good work.

[smilecolorsan]

you are like magical! I am doing this stuff RIGHT NOW! Yes @yucky1336, great timing! :)

Thanks a lot sir!

[yucky1336]

man great timing. i just learned this lesson today. love you man

[O0oSorousho0O]

Hey are you in 1st year university... your video upload dates seem to be following my curriculum ever since I was in grade 11 lol

[UnicornOnTheCob16]

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

[patrickJMT]

@UnicornOnTheCob16 nah, more like a good TA

[UnicornOnTheCob16]

@patrickJMT haha Regardless, you're a big help, and for that, I thank you.  Cheers,

[rokz991]

oO

[PensadorChileno]

i didnt understand a SHIT...

dont worry im not an idiot im just 16 years old...hahahah



[shimiikimimuy]

@PensadorChileno doesn't mean you still can't understand.. hahaha i'm 16 too?

[youareuncoolhotmail]

well my mind = blown

[imnoobshit]

Thank you very much! Patrick 

[vickiormindyb]

Honestly, the only thing I know about theta is that it's a sleep-wave brain pattern.

I'm a paramedic and we've never needed trigonometry to pass Paramedic School.

But it helps w/ IV therapy to know as much math as possible, b/c I.V. Therapy is all math and nothing else.

Which annoys me but is why I had to find YT videos about these calculations.

It helps.

[Matee1995Rehman]

I'm so gonna get an "A" tomorrow...thanks Patrick..:)

[Puggalug]

This example actually doesn't necessarily need trigonometric substitution. If you take an x from the x^3 and put it next to the dx (which would make the numerator x^2), you can then use u-substitution.

Let u = 16 - x^2, x^2 = 16 - u, which means 2x dx = (-1) du, or x dx = (-1/2) du.

You can then replace the numerator with (16 - u), the denominator with sqrt(u), and the dx with (-1/2) du, and it then becomes the matter of using the reverse power rule after some algebraic manipulation.

[patrickJMT]

@Puggalug yep, this is true!

[Puggalug]

@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?

[mightymanlap]

@Puggalug

yea that's the way i got that.

at first the method in the video looks odd but it's works and similar to the way i got taught

[WUTCHA1197]

@Puggalug

The point of this video is to teach Trigonometric Substitution lol, and this example happened to be a good one for it, even though it can be solved via other means.

[endesigner]

Amen brother. That was one hell of a solution. Also as someone pointed out, more statistics would be highly appreciated :)

[mepicaelsobaco]

Dear patrick, I have been checking your channel and I found out that you do not have many videos on distributions, could you please do some videos about those? f.e. geometric distribution, hypergeometric, binomial and such.

I am having a subject called probability and statistics in Norway and my norwegian is not the best so I could really use your videos a lot! thank you in advance keep up the good work! ;D

[zloyhimik]

can't we use arcsin, arctan and stuff at the end to get the value of THETA?

[patrickJMT]

@zloyhimik typically people do not want to see it this way; using the right triangle produces a much more simple equation

[Halo3ForumEurope]

@zloyhimik The point isn't to find the value of theta, it's to integrate x over root 16 - x^2

[pabloMTv]

dear patrick, thank you for uploading this i thought you forgot about youtube. i miss you. oh so very much! ty :)

[patrickJMT]

@pabloMTv ha, nice to see i am missed. i was actually spending some time getting things organized (playlists and stuff) and also working on trying to get some iphone apps out (almost there!). so, i have been doing stuff, just not creating new videos, which is unfortunate, as i hate organizing and like making videos. c'est la vie though, it is stuff that needs to get done!

hope you are doing well!!