Double and Triple Integrals

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Double and Triple Integrals

Рет қаралды 523,104

5 жыл бұрын

Remember the good old calculus days, and all that time we spent with integration? Let's go back! Oh calm down, it wasn't that bad. Besides, we won't be learning anything terribly new, we will just look at double integrals and triple integrals, which are pretty much the same as single integrals, we just integrate more than once. But admittedly it can be a little tricky to set up the bounds of integration and choose the order in which we integrate each variable, so let's go through the rules and some examples.
Script by Howard Whittle
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Пікірлер: 389

@GiangTranAI 4 жыл бұрын

Best teachers so far: 3blue1brown and Professor Dave.

@hzkzg1614 4 жыл бұрын

You seriously wouldnt count sal or Patrickjmt?

@adityarajsrivastava6580 4 жыл бұрын

Blackpenredpen

@garethpienaar3119 4 жыл бұрын

Professor Leonard is the best for me, by far

@gouravgope1367 3 жыл бұрын

Zach star

@jorge_cazares 3 жыл бұрын

For me, the best teachers so far are: Professor Gross, from MIT OCW Calculus Revisited, 3blue1brown, and Professor Dave

@schifoso 5 жыл бұрын

You are such a great teacher. And I like how you use "we" instead of "you". Makes the student feel like they are not alone.

@MegaYoungscientist 3 жыл бұрын

I think it's great because even the professors still are students at the end of the day, because everyone is still learning more about their subjects.

@akuo0708 4 ай бұрын

this is the clearest explaining math video i've ever watched

@mastershooter64 5 жыл бұрын

So you can actually find the volume inside a tesseract niceees

@kek3324 5 жыл бұрын

its a hypervolume

@JorgetePanete 5 жыл бұрын

@@kek3324 It's*

@doxo9597 5 жыл бұрын

Jorge C. M. I can tell you have a lot of friends.

@OneDerscoreOneder 5 жыл бұрын

It’s just all the side lengths multiplied

@dinamosflams 4 жыл бұрын

You can find both, the volume and the hypervolume of a tesseract. Although I think it's more difficult to grasp the concept of the volume of a tesseract

@buttersquids Жыл бұрын

I was struggling a lot on understanding double integrals on a homework assignment, but this helped massively. Thanks Dave!

@theresaread6174 3 жыл бұрын

Blessings upon you, Dave. Two minutes in and you’ve already made this make more sense than my instructor.

@mikepablo 4 жыл бұрын

Brilliant , wish I had this when I did maths so much clearer and simple, during lock down going though my old notes 30 years ago inspired me to study more

@FlyByPC 5 жыл бұрын

Great explanation! Of course, my inclination is still to hit it with a FOR loop...

@ActionJaxonH 5 жыл бұрын

This video is amazing. I’m self taught, going through Professor Leonard’s Calc 3 YT series course, and double and triple integrals are coming up in the very near future so I wanted to get a head start. This is totally logical and it just makes sense

@extremeforlife8563 2 жыл бұрын

Thanks, I checked out the series after seeing your comment. It is more suited to what I am looking for. Really appreciate it man.

@harishkumar-rn2mw 3 жыл бұрын

Hi Dave, I got confused in the part choosing lower bound and upper bound between 2 cuves. Pls explain..

@georgefan2977 5 жыл бұрын

Thank you, that was one of the most straightfoward explaination!

@lemonhscott7667 6 ай бұрын

Professor Dave, thank you so much for these resources! They've been a huge help to me in ODELA and Vector Calc. I'd be lost without you!

@lukafarkas420 Жыл бұрын

good job Dave, you have explained this to me in a most understandable way possible, with clear color indications, thank you sir.

@coop_the_troop 3 жыл бұрын

Man I’m trying to learn first calculus, I was recommended this from a friend in the math field to help, it seems a bit to daunting, I wish I was I just good at math and actually understood what he is talking about most of the time

@ProfessorDaveExplains 3 жыл бұрын

Start the calculus playlist from the very beginning and all will make sense!

@cd8836 11 ай бұрын

Thank you for the videos. They help a lot! I’ve had a mental block about these topics for decades.

@tanishq1026 2 жыл бұрын

Thank you so much! I really appreciate this as we don't get taught a lot of concepts and underlying principles in math, so this just makes the subject so much more interesting. :)

@sine4859 2 жыл бұрын

wow i didnt expect integrals to have this much depth to them... how can you not love math, omg great video btw :)

@krishlapatra424 5 жыл бұрын

Really nice ... So clear concept.... Thank you professor Dave

@jocelyneavila6870 4 жыл бұрын

Thank you for the subtitles in English! It makes it much easier to follow-up.

@md.azmiribneislam6885 4 жыл бұрын

Nice work... You deserve a big big big thanks... Go ahead Dave brother

@melontusk7358 4 жыл бұрын

I've finally done it. Thanks for your help, my good sir. I'm a lot more confident now.

@chroma9848 5 жыл бұрын

You're an excellent teacher, you truly are. I survived 1st year of engineering with your help. It would be nice if you can make videos on differential equations 😅

@shaiyongcheng9721 4 жыл бұрын

This video is better than 1 hour of lecture. Tq very much

@mkpr757 2 жыл бұрын

A video masterpiece. Grateful for the illustrations, painted a clearer picture in my mind...

@werkatfischer3183 3 жыл бұрын

This is probably the best that this video could possibly have been made.

@huijiang3051 2 жыл бұрын

Thanks Dave, you are a wonderful professor!👍

@dalibormaksimovic6399 Жыл бұрын

Thats the most outstanding explanation I ever got. Thank you so much!

@johnsnow3444 4 ай бұрын

Was so thrilled when i did the double integral the other way from y/2 to (y)^1/2 and got the same answer! strangely that way took up less paper. Thanks for the solid content!

@thabolikotsi5765 5 жыл бұрын

awesome vid thanks im a fresher ive jusst started self learning ths topic ths will help wth understanding

@sauravkr.mahato 2 жыл бұрын

Great Visualization of the figure formed by double integration Loved it !!

@aceflamez00 5 жыл бұрын

Wow that was easier then expected. Thank you for explaining it well.

@bryanwharton6692 5 жыл бұрын

“Performing multiple integrations is not all that daunting, on the SURFACE!!” Haha

@ndereratjijahura2048 2 жыл бұрын

Thanks so much for a clear presentation.

@wompwomf 2 жыл бұрын

whenever my dad checks up on me if im doing work, i just pull up your videos and he doesnt question it! thank you :D

@encinaallaineharleya.8586 Жыл бұрын

We have a calc quiz tomorrow and this video sure helps, Thanks!

@ejticomon9603 Жыл бұрын

Why is the y integral from x^2 to 2x and not 2x to x^2?

@lolzdatguy4987 4 ай бұрын

Lower relative to y

@sudharakafernando4391 3 жыл бұрын

Professor Dave is the best...thank you very much!!!!

@millieh3179 5 жыл бұрын

Can you do a video on Green's, Stokes' and Gauss' Theorems?

@Preparing_and_Testing 5 жыл бұрын

Could you send me notes of divergence theorem ?

@ProfessorDaveExplains 5 жыл бұрын

Millie all three of those are filmed, animated, uploaded, and to be released very soon!

@GeoRaphaelMichael 3 жыл бұрын

@lulu , your wicked tactics to paint real Christians ain't gonna work, people like you are the reason muslims conflate legitimate love lead criticism from people like David Wood and Robert Spencer with hatred from people like you and richard spencer.

@awesomecodeyay8382 3 жыл бұрын

20UPH512_Geo Raphael Michael What was lulu’s comment about?

@ivoryas1696 10 ай бұрын

@@GeoRaphaelMichael *_Bruh, what_*

@stonerambo3982 8 ай бұрын

I was only confused in one step it got cleared only within first 2 minutes...

@nosirrahonline1225 Жыл бұрын

Oh my god, thank you so much for this video. The videos that I get for my class gave me an example where both y and x's bounds were 1 so I didn't understand how she was doing it.

@someone________2502 2 жыл бұрын

Great video. Even though I only did high school calculus I could still follow what he is saying.

@cboaitey99 5 жыл бұрын

Thanks so much! I never understood this in my Engineering lectures, now it makes sense.

@os9458 5 жыл бұрын

Hi Rosal.can I know is this thing involve I'm grade 12 or higher grade .Because I'm going to do engineering too. Currently grade 12

@cboaitey99 5 жыл бұрын

OsJ I’m not sure, I studied this in university.

@Zephyr-tg9hu 4 жыл бұрын

Thank you so much, Dave! You are and always have been a lifesaver.

@annea1537 6 ай бұрын

Danke sehr!!! 🎊 beste Erklärung! Mit Abbildungen, klar und deutlich. ❤❤❤❤❤

@andreacondello 2 жыл бұрын

that is amazing how clear you was

@mavlonkarlsefni 3 ай бұрын

I have a test tomorrow, and your video really helped me to understand integration more deeply. Thanks from Russia!

@darkwing2924 2 жыл бұрын

Thanks for making calculus fun and interesting

@NoctuaStrigiformes 5 жыл бұрын

Integrals are tight. You made it look super easy, barely an inconvenience.

@TTeach22 Жыл бұрын

Great thought and too clear fellow style, I apricate your way of explains

@christosgolsouzidis1286 4 жыл бұрын

I thought that double integrals give the area of the surface of a function and triple integrals the volume of a function respectively

@tzonic8655 3 жыл бұрын

Και εγώ ρε φίλε,έτσι δεν λέει και ο γκαρουτσος? 😂

@virajpatel2121 2 жыл бұрын

Sir you are awesome ,I love your explanation method. 😇😇😇

@user-fo8cu6ef5y Жыл бұрын

You're the E of the mc²! Great lecture. Congrats.

@itsme.01 10 ай бұрын

In the first comprehension, when we move from 2 to 3 in x,then y=x+1 is lower to 2x . Why we consider here limit in y from 2x to (x+1)?

@jacobridley8156 Жыл бұрын

so helpful cheers Dave

@ItIsMe167 4 жыл бұрын

Good Job, Thanks for Sharing

@astroflexx82 Жыл бұрын

Amazing video!

@kamalnath4606 8 ай бұрын

love you professor dave

@hexagor5140 3 ай бұрын

Thank you sm genuinely

@alexanderkaiser89 2 жыл бұрын

Hi Professor Dave. I have a request that you may find interesting or not, it’s a mathematical one. I have always found it hard to understand “Inter-universal Teichmüller theory”, “The Collatz Conjecture”, and “The Birch and Swinnerton-Dyer Conjecture”. If you would make a video on one of these topics that would really help 😊 I’m studying a Master’s in mathematics in Denmark. I’m sorry for my English, I’m not mothertongue in English. Btw, I love your content.

@mohitchaurasia7181 5 жыл бұрын

💥👌Nice explanation 💥👌☺️🤗

@amaizasafdar9401 3 жыл бұрын

no word to explain your efforts may God reward this

@henryy6918 4 жыл бұрын

Wonderful video.

@didyk3574 4 жыл бұрын

Hey dave can you graph this function in 3D f(x,y)=xy/(x^2-y^2) around the point(0,0)

@TemplarX2001 4 жыл бұрын

annnnnnnnnnnnnnd you have a new sub/ bingewatcher

@Jack-lp4jd Жыл бұрын

Best explanation around. Though im still struggling to understand how taking the integral of the x-y plane in two different ways gives volume. So the area under the curve given from the first integral just happens to also equal the volume?

@jainyshah3000 4 жыл бұрын

Brilliant! Thanks :)

@pankajpokhrel2463 4 жыл бұрын

Very well explained..

@thefatcat1997 4 жыл бұрын

I wish i had u as my teacher during my btech...

@HorizonSpeed26 4 жыл бұрын

Thanks very useful and understandable

@deltaexplorer47 4 жыл бұрын

WOW !! THANK YOU VERY VERY MUCH !!

@aloischipfurutse5079 3 жыл бұрын

I still don't understand why someone can dislike a video like this :( You are incredible!

@dellpi3911 3 жыл бұрын

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@user-cq2cd1xc9h 7 күн бұрын

Thank you, so much

@adristimaulidafauzi4418 3 жыл бұрын

Finally I understand the sense behind these

@taladiv3415 3 жыл бұрын

Dave the man!

@kaymoneyalottoww4828 5 ай бұрын

cool teacher, straight to the point

@9silentufo9 4 жыл бұрын

Great video

@prateek3828 Жыл бұрын

I thank you dear sir for mentoring me . 🙏

@leedsoldat4189 3 ай бұрын

A learner from Tanzania,🤝you are a good teacher ❤

@musthafamb1757 4 жыл бұрын

Great teacher

@STKeTcH 3 жыл бұрын

You the man, man!

@chandraprakash934 4 жыл бұрын

very good , thanks !

@nirodlowe1615 Жыл бұрын

Just keep it up professor!🥳🥳🥳

@freezinfire 2 жыл бұрын

Thank you very much.

@gk2772 16 күн бұрын

Just amazing

@eskayML Жыл бұрын

I have a question please For the upper and lower bounds isn't the x² greater than 2x and why didn't it get placed at the upper bound instead?.

@pakshah5449 6 ай бұрын

Thanks Great Video

@pawanmarahatta5749 2 ай бұрын

blessings upon you, Dave.

@mayashomarieh7941 Жыл бұрын

Thank you so much

@ramuganesan 2 жыл бұрын

at 07:12 , how do you say that y runs from the lower curve to upper curve? sir i cant understand that point

@kerryloh5285 8 ай бұрын

Nice explaination

@JorgetePanete 5 жыл бұрын

1:37 I think there are counterexamples to that statement, but it works in general.

@paulespettia4949 5 жыл бұрын

Could you tell pls

@mohammadtorikh Жыл бұрын

Thank you sir

@azadprasad856 3 жыл бұрын

He does know all about science stuff......... professor Dave Explains ❤️❤️❤️🔥🔥🔥. I Love this😎

@official_darick 11 ай бұрын

Hello Professor, please can you cross check you final solution to the calculation on volume integral: 3x2 - 3xy2.

@paulgbago4586 4 жыл бұрын

hello can explain how you take x^2 as the lowest value for a integral and another integral. what makes them the upper value on y and lowest value on x ?can you make it more clear cause i tried to find why but still cant find out . At first i thought it was cause the 2x function was above the x^2 from 0 to 2. thanks you

@yuel.5013 4 жыл бұрын

You're right, depends on the sign. Solve sqrt(y) >= y/2, it's true on [0; 4].

@student_0224 3 жыл бұрын

Thanks a lot sir....

@extremelearning3113 2 жыл бұрын

It's an excellent explation.

@webstar9845852491 3 жыл бұрын

Awesome video. Could you also explain how does a double integral change if converted to cylindrical and polar coordinates?

@carultch 2 жыл бұрын

For cylindrical coordinates: instead of slicing bread (rectangular coordinates), we are slicing a cake. For spherical coordinates: instead of slicing bread or a cake, we are slicing a planet into longitude and latitude "squares".