Double and Triple Integrals

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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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Опубликовано:

20 авг 2019

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Комментарии : 371

@schifoso 4 года назад

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 года назад

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.

@GiangTranAI 4 года назад

Best teachers so far: 3blue1brown and Professor Dave.

@hzkzg1614 4 года назад

You seriously wouldnt count sal or Patrickjmt?

@adityarajsrivastava6580 4 года назад

Blackpenredpen

@garethpienaar3119 4 года назад

Professor Leonard is the best for me, by far

@gouravgope1367 3 года назад

Zach star

@jorge_cazares 3 года назад

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

@buttersquids Год назад

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

@mastershooter64 4 года назад

So you can actually find the volume inside a tesseract niceees

@kek3324 4 года назад

its a hypervolume

@JorgetePanete 4 года назад

@@kek3324 It's*

@doxo9597 4 года назад

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

@OneDerscoreOneder 4 года назад

It’s just all the side lengths multiplied

@dinamosflams 4 года назад

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

@theresaread6174 3 года назад

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

@akuo0708 2 месяца назад

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

@mikepablo 4 года назад

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

@ActionJaxonH 4 года назад

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 Год назад

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

@FlyByPC 4 года назад

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

@lemonhscott7667 5 месяцев назад

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!

@georgefan2977 4 года назад

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

@melontusk7358 4 года назад

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

@harishkumar-rn2mw 3 года назад

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

@coop_the_troop 3 года назад

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 года назад

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

@lukafarkas420 Год назад

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

@jocelyneavila6870 3 года назад

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

@cd8836 10 месяцев назад

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

@werkatfischer3183 3 года назад

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

@sine4859 2 года назад

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

@shaiyongcheng9721 4 года назад

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

@johnsnow3444 3 месяца назад

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!

@chroma9848 4 года назад

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 😅

@tanishq1026 2 года назад

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. :)

@mohamedamr6228 3 года назад

You are a GENIUS...Such a relief to finally understand the bounds depending on variables... thanks for your hardwork really appreciate it

@dellpi3911 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-IangXACFW48.html

@mkpr757 2 года назад

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

@fightinggod03 2 года назад

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

@krishlapatra424 4 года назад

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

@NoctuaStrigiformes 4 года назад

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

@sauravkr.mahato 2 года назад

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

@mavlonkarlsefni 2 месяца назад

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

@andreacondello 2 года назад

that is amazing how clear you was

@aceflamez00 4 года назад

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

@encinaallaineharleya.8586 Год назад

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

@millieh3179 4 года назад

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

@Universities_Reels 4 года назад

Could you send me notes of divergence theorem ?

@ProfessorDaveExplains 4 года назад

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

@GeoRaphaelMichael 3 года назад

@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 года назад

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

@ivoryas1696 8 месяцев назад

@@GeoRaphaelMichael *_Bruh, what_*

@bryanwharton6692 4 года назад

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

@dalibormaksimovic6399 Год назад

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

@nosirrahonline1225 Год назад

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.

@md.azmiribneislam6885 4 года назад

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

@thabolikotsi5765 4 года назад

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

@huijiang3051 2 года назад

Thanks Dave, you are a wonderful professor!👍

@christianb4679 4 года назад

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

@os9458 4 года назад

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

@christianb4679 4 года назад

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

@someone________2502 2 года назад

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

@user-fo8cu6ef5y 11 месяцев назад

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

@alexanderkaiser89 2 года назад

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.

@Jack-lp4jd Год назад

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?

@annea1537 5 месяцев назад

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

@Zephyr-tg9hu 4 года назад

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

@amaizasafdar9401 3 года назад

no word to explain your efforts may God reward this

@ndereratjijahura2048 2 года назад

Thanks so much for a clear presentation.

@thefatcat1997 4 года назад

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

@darkwing2924 2 года назад

Thanks for making calculus fun and interesting

@sudharakafernando4391 3 года назад

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

@aloischipfurutse5079 3 года назад

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

@dellpi3911 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-IangXACFW48.html

@leedsoldat4189 2 месяца назад

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

@JorgetePanete 4 года назад

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

@paulespettia4949 4 года назад

Could you tell pls

@ejticomon9603 Год назад

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

@lolzdatguy4987 3 месяца назад

Lower relative to y

@TTeach22 Год назад

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

@adristimaulidafauzi4418 3 года назад

Finally I understand the sense behind these

@christosgolsouzidis1286 4 года назад

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 года назад

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

@pawanmarahatta5749 Месяц назад

blessings upon you, Dave.

@virajpatel2121 2 года назад

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

@didyk3574 4 года назад

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

@itsme.01 9 месяцев назад

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)?

@stonerambo3982 7 месяцев назад

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

@webstar9845852491 3 года назад

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

@carultch Год назад

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".

@eskayML Год назад

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?.

@kaymoneyalottoww4828 4 месяца назад

cool teacher, straight to the point

@TemplarX2001 4 года назад

annnnnnnnnnnnnnd you have a new sub/ bingewatcher

@danielvolinski8319 2 года назад

14:30 The first example on the Checking comprehension is wrong: the internal integral boundaries should be from x+1 to 2x

@ItIsMe167 4 года назад

Good Job, Thanks for Sharing

@hexagor5140 2 месяца назад

Thank you sm genuinely

@jacobridley8156 Год назад

so helpful cheers Dave

@prateek3828 Год назад

I thank you dear sir for mentoring me . 🙏

@paulgbago4586 4 года назад

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 года назад

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

@ramuganesan 2 года назад

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

@kamalnath4606 7 месяцев назад

love you professor dave

@kerryloh5285 7 месяцев назад

Nice explaination

@AmanT241 2 года назад

oh men i wish i knew you back when i was taking Applied maths 2 in college

@pankajpokhrel2463 4 года назад

Very well explained..

@azadprasad856 3 года назад

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

@lordyabo9910 Год назад

Can someone please explain why the curve y=2x is greater than the curve y=x^2? Thanks in advance!

@SMNAviation 3 года назад

I consider the view count on this an insult. And an even greater one, that 52 people dare dislike it. Dave, your videos are amazing.

@henryy6918 4 года назад

Wonderful video.

@clarkpeng1008 4 года назад

what if the functions defining the bounds overlaps more then once? Like sin(x) and x/2 then how do you determine the lower and upper bound?

@ProfessorDaveExplains 4 года назад

Ooh that's a good question. I suppose in such a case you would split it up into multiple integrals.

@jackrubin6303 3 года назад

If you look at f(x,y) = 1+ 4xy example, if you just look at solid by itself and compute volume without using complex integration, for x = 1 (1-0), y = 2, (3-1), and z = 1 + (4*1*2) = 9, I get a volume of 1*2*9=18. Where did I got wrong?

@thanhavictus 2 года назад

It would really help if you had shown what these xy functions actually look like in 3 dimensions

@4tytude 3 года назад

hi professor dave, in 4:00 you said 10 is the volume under that given example surface, why does it considered "under" not "above"?

@arjunmanoj9687 2 года назад

Hi Dave. I loved the video, it was a great explanation and helped me understand double integrals a lot better. I had a question regarding the problem that was solved at the 5 min mark. You mentioned that when integrating for dy first, we need to take upper bound to be x^2 and lower bound to be 2x (at 8:21 mark). But when you solve the problem, the upper and lower bounds were swapped i.e. upper was 2x and lower was x^2. Was there a mistake here?

@tcy101 2 года назад

I believe it is correct as it is in the video. I think he means lower and higher in terms of y. E.g. x^2 is lower on the y axis than 2x

@manishs6479 4 года назад

This is pretty cool. But how does this look when you take indefinite integrals? I ask because you specifically mention that the outer bounds have to be constants. Are double integrated expressions just really messy expressions in x and y? Not studying this in school but it's much cooler than i thought it would be and I want to learn more.

@FearDeniesFate 4 года назад

Yeah, they just become messy expressions because you never insert numbers so it can get out of hand real fast. To give a supper simple example, consider this definite integral: int[x=0..2]( 2*x ) = 2^2-0^2=4 Compared to the indefinite integral: int (2*x) = x^2 The definite integral gives an area from 0 to 2, the indefinite gives an expression.

@official_darick 10 месяцев назад

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

@mlop2484 9 месяцев назад

thank you sir

@HorizonSpeed26 4 года назад

Thanks very useful and understandable

@cabbageman 4 года назад

How is most of the volume beneath the xy plain? What are the bounds in the z dimension?

@millieh3179 4 года назад

z = f(x,y) = 3x^2-3xy^2. You'd have to look for critical points/saddle points etc. using the gradient vector. Or you can type the equation into wolfram alpha, which will provide you with a 3d model of the surface. From there you can see the surface slopes downwards and at (2,4) you have a local minimum. Knowing this information you can just input the coordinates. z=f(2,4)=-84 for the lower boundary. z=f(2,0)=12 for the upper boundary