Triple Integrals, Changing the Order of Integration, Part 1 of 3

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Triple Integrals, Changing the Order of Integration, Part 1 of 3. In this video, I start discussing how a particular order of integration for a given region and integral ' makes sense '! Then I go about changing the order of integration. In this part, we integrate with respect to z first.

[@chandlerinman4393]

I just wanted to let you know that I have watched your videos for explanations from AB high school calculus all the way up to now, 6 years later, where I am pursuing an economics P.H.D. at the university of Michigan. Thank you so much for all the help over the years!

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lol first wedding

[@theunraveller4171]

So much racism in here. Such a shame

[@Xxmortal9xX]

Man I graduated with my EE degree 2 years ago and PJMT was the best source to build a strong fundamental in calculus. All these videos bring back great nostalgia. Much love Pat!

[@patrickjmt]

thanks for the kind words :)

[@masoncdyer]

Dude idk how you do it. You are hands down the best teacher I have ever known; amazing job as always man. Thank you :)

[@zedlepplin9450]

+Mason Dyer I know dude, once I become an engr, ill give back to this guy!!!!!

[@StefCrl]

There's a special place in Heaven reserved for people like you!!!!

[@daisyflat]

Final in 12 hours, and yet again this is the best review channel. You should be given all of the awards and all of the trophies.

[@24overthetop]

you are the best calclus instructor in youtube history

[@ruthjin5461]

almost 10 years and this is still very helpful!

[@ballwizz23]

These videos will go down in history. Some day we won't need calc classes. Our kids will just watch these videos instead.

[@jaywong2583]

you are a legend, how have u not won an award for legendary explanation?

[@RayanMADAO]

I remember hating doing these when I took calc 2 but Im reviewing triple integrals and for some reason seeing these shapes in space and figuring out the limits is fun to me now

[@BFMert]

I loved the way you explain how Z's bottom limit comes!

[@tylerpaquin1753]

First time coming across this channel, the best decision I've made all day today.

[@LEE942K10]

Patrick, unbelievable videos! Would not have passed first year calculus in college if it wasn't for you, please keep it up, thank you man!

[@eday00]

When I talk to other students about how they study for Calc, your name comes up often. Thank you for helping so many of us.

[@MuhammadUsamaQamar]

I need Patrick not in Maths but in my all subjects what a teacher *_*

[@tehJimmyy]

You are a god. My teacher need 9 hours to explain this in 3 weeks you did in 30 minutes total.Just ridiculous.

[@rafaelcrispinalejandrino6771]

Not all American Heroes need to go to boot camp. I salute you sir!

[@taladiv3415]

Good clear explanation Patrick. Thank you for helping us students, studying at institutions robbing us of our money while offering little more than an expensive examination service!

[@Silliestofgeese]

This was a beautiful explanation, thanks sir i love math but sometimes professors just don't make it easy for students. You put things in a way that is so unbelievably easy to understand. Thanks again.

[@Prashant873]

recently i watched video of double and triple integral solution ...it has cleared my all doubts ,certainly it helped me lot ....i m feeling sense of enlightment ,nt a single question is being left ..... extremely thanks

[@29thedream]

could you make a video on how to draw these surfaces?

[@syd_jzx100]

Sketching these is in a realm much easier than this.

[@stephaniehiggins6820]

My professor spent several hours desperately trying to explain what you just easily did in minutes, thank you so much! Feeling better about my upcoming exam :D

[@lanakamal8369]

I can’t thank you enough 😭😭 I couldn’t have made it without you really just know that you are awesome. Your existence is just beautiful 😀❤️❤️

[@saad.hussain.]

TY MA DUDE. THE IMAGINARY LINE MADE IT ALL MAKE SENSE FOR THE LIMITS OF INTEGRATION FOR THE INNERMOST INTEGRAL

[@paulringab123]

been through calc1,2,3,differential equation and got over B's for them all thanks to this genius.

[@Ranskire]

Patrick, thank you so much. Triple integrals has been one of the most challenging topics in calculus so far for me. I like how you explain how the original integral was obtained. I think students (like myself) get confused on this first step, and end up not understanding how to change the order of integration from there. Thanks for doing what you do. :)

[@TonyTorzido]

You helped me develop a wrinkle in my brain, good sir.

[@bobseagull7600]

You got solid Sharpy skill man.

[@robottoy194]

This man is taking me through 2nd year varsity! Thank you and keep up the good work

[@ter890]

I love your videos. You make even the most tedious math seem like a walk in the park.

[@100yrsdeath]

5 years later you the best

[@joannanicholson2540]

Thank you. Again, you are are the best. I get it. Finally.

[@favio2491]

+Joanna Nicholson finally....

[@patrickjmt]

glad i could help :) just spread the word about the videos and that will be thanks enough :)

[@patrickjmt]

no. if in single variable calculus i said: you will be integrating a function from x = 0 to x = 4. what is the function? you have no idea based on the limits only. it is the same idea here.

[@nickspong4862]

Thank you Patrick.

[@johnbatchler8551]

thanks I understood it the first time. I went back to see the video back and pick up the rest

[@jenoharu]

thank you for all your vids! im on my last math course in our math series

[@davlatbekkobiljonov911]

great explanation, thanks

[@rorythompson864]

Sick explanation man, ur actually the goat

[@GetCronk]

Thank you for all your help! You've helped me through most of my undergraduate education!

[@carlosenriqueulloa]

I (and my grade) thank you!

[@sei4633]

It does make sense!!! Finally!! Thank you so much!

[@natureshorts6657]

This was very helpful. Thank you.

[@ghanashyam8461]

it was just mind blowing !!! I finally understood how to solve a triple integral!!!! thank you so much : )))))))

[@trimmien2350]

Guys! I think I'm ready to watch Rick and Morty!

[@SoulSlick88]

Well played sir, well played. Thanks for this!

[@josiahmcdonald3500]

you made this seem easy. Before I watched I had NO idea what was going on. Thanks so much.

[@maaaaddieee]

You really are awesome. Thanks for all of your videos they are so, so, so appreciated. They've gotten me through 3 quarters of Calc so far! I'm on my fourth now, and these vids continue to save my ass every day!

[@DoggoWillink]

If you know the bounds of integration for each variable than you don't need a picture.

[@soxxks]

Dude. You're the best.

[@3bdullah830]

thanks a lot dude !! you are much better than my professor !!

[@DANGJOS]

Thank you!! I wish my professor would take more time to explain things like you do

[@ehsanziaee1183]

You are amazing man! I always pray for you.

[@divyanshushankar2147]

At 4:00, for the limits z would be a function of y only. We consider the shadow of the domain on the y-z plane so X=0 for the limits.

[@enesburaksen8960]

I can understand so obvious thanks to your magic hands.Tkank u man :)

[@matthiasandersen3329]

Awesome subject. Sadly neglected in most calc courses. Awesome video!

[@violinsheetmusicblog]

Yeah, I realized that. This was pretty tough, but this video still helped alot.

[@pennydave]

you are a very amazing person. I see why you would have to wear your wedding ring in your videos. thanks patrick

[@NucksSuckBalls]

You're a life saver, great videos

[@DoggoWillink]

And also, the way you make a 3space graph is by first looking at the shape made in each plane. Look at the xy plane, xz plane, and yz plane. Once you do that, it isn't hard to figure out, depending on the graph. After that, get all the intercepts and as many points as you can, and it should come out decent enough. That's how I do it, anyway.

[@alex1993seattle]

I will have my final in about 10 days, wish me good luck!!!

[@MahiMahi-jz6fp]

Aamin

[@titaniumlibra]

The way I understand triple integrals is that now you are finding out information about the volume, rather than finding the volume itself. When you took a double integral you were finding the volume from the area, and a single integral was finding area from an interval. The mass is a quality of the volume which can change, depending on the density of that volume. It doesn't have to be mass, though, I don't think. I would imagine it could be heat or energy or something other quality that a volume might have.

[@aarontainter]

PatrickJ, you're my man!

[@aminoditide]

very detailed, and very very very helpful!

[@abdullaalbaloushi5691]

thanks Patrick for making triple integration easier, i was wondering if you can upload a video about "Average Value of a Function of Three Variables"

[@rockyguinto2325]

hi whats up buddy.. I have to say you did a very great job helping people that struggle with maths and for some people like myself who is quite preoccupied with daily stuffs yet whenever i do have spare time i race to my book and notes to learn math again- so i find your channel very very very useful and we are very grateful for that.. ^^ if could request you something bro is that, im working my way up to calculus here my man, hoping next year or 2 years id be able to get back to University,. thats why little by little i want to self-learn so if that time comes things would be easier.. hence asking you a big favor if you could just give me an outline on which of your videos to go first- that would make my learning be more organize. i mean, if i go algebra then trigo etc,. coz im embarass to admit that most of the playlist you created sounds all greek to me.. :( so there, bro if you could spare time helping a brother in need.. i promise you my engineering diploma. thanks. many many thanks.

[@carloschutz4247]

thank for the video, greeting from Chile

[@omarbaik93]

you deserve a Nobel

[@Joslinmeister]

Well explained. Much gratitude!

[@natashaws014]

this guy is my soulmate

[@blve781]

Thank you.

[@joefuertes8455]

Thank you so much for this video!

[@Prashant873]

thanx patrick......

[@xkaili]

Can we one day, in a random video, see the face of our math savior?

[@solomunallouche8425]

this is great but can you show a vid on how to change the first bound as well for example dz to dx? thanks

[@iffatzaidi2052]

thanks bro. really help me about this topic.

[@richsauce5558]

Real master

[@BennyRJ]

Gran video, de mucha ayuda

[@IoIwhut]

What i didn't understood in class after 2 hours of lecturing became clear in less than 6 minutes. What kind of dark magic is this??!!

[@RahulDas-gk4zi]

my trick : if i have to integrate wrt to dx then i draw a strip parellel tp x direction and then see which curves are surrounding the stip and then reprenst my bounds in term of those curves

[@circleofthytyrants]

really helps!

[@myshitez]

I have an assignment where I have to draw the region of integration with a triple integral in dzdydx order, and I am having major trouble with it, but this does help.

[@BobClemintime]

I think the volume is lower in this video than some of your others for some reason. Also, would be nice if you did some videos with more complicated shapes and possibly use cylindrical and spherical coordinates. Thanks for all the great videos though.

[@Neiliean730]

i hope sharpie gives you some sort of money for advertising their products in your videos

[@zaneb808]

ARE YOU THE GUY THAT DOES THE EXAMPLES ON WEBASSIGN?!?!?

[@JollyConcrete]

hallelujah I've been saved

[@samvenker3137]

Why wouldn't the Z line also go through the "tent" function, or why wouldn't some of the Z coordinates start along the tent and continue to the roof, if it goes "into" the volume space so to speak.

[@mhamedchaim7508]

شكرا جزيلا

[@Mygeto4]

What if I don't have a picture to reference? I'm only given my triple integral with the ranges each variable is integrated from. I knew how to draw them out for double integrals but adding the Z is really hurting my perception.

[@micky9217]

see that would be cool, but my smart teacher does not provide the graph. Most of us students can graph on the x,y plane but when the z comes in, we give up and miss the question, could you please show us how to graph those only given the triple integral?

[@engineerhere1061]

U r awesome bro 😍😘😅

[@pawanchoure1289]

It's very useful

[@ICOD73]

Nice Drawing

[@loganmasters3507]

You're the man

[@GetCronk]

With the limits of integration given, you can simply graph it yourself and visualize whats going on.

[@TheIlliberal]

thanks so much man .....

[@JKhal]

THANK YOU

[@jaimeandresgarcia7518]

Thanks a lot!

[@DANGJOS]

you can determine the region from the limits but not the function