How to Set Up Double Integrals

Double integrals can be used to find the volume under a surface, but how exactly do they work and how do you set one up?
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This video was funded by Texas A&M University as part of the Enhancing Online Courses grant.
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The animations in this video were mostly made with a homemade Python library called "Morpho". You can find the project here:
github.com/morpho-matters/mor...

[@4thalt]

did I just stumble upon Morphocular's old channel

[@hydropage2855]

I knew this voice seemed too familiar I just couldn’t tell from where

[@clarabartusiak4540]

As a very visual math learner, this is the best video I've seen explaining double integrals -- priceless.😭🙏

[@willyh.r.1216]

For me, this is the best visual explanation of double integrals. Thank you.

[@10-den-see]

Couldnt sleep...its 3:30 AM was thinking about what could possibly be a practical use of double integrals...or how do they work to solve a practical problem....and there you go....found the perfect vid

[@ilgnsogut3715]

These A&M videos are the best, perfect visualization

[@clayton97330]

This is magnificient! This is the perfect way to explain this concept.

[@AliEgemenB]

This is legit the best video on this topic. Awesome work.

[@abhinnkaushik6534]

this explained such a complicated idea beautifully.

[@ulisespachecosanchez5058]

More than important to understand the dimentions in the double integres, thank you

[@dominiclederer9564]

Im a visual learner and this was incredibly helpful, thank you !

[@arims8346]

you had just saved my whole semester, thank you sooo muuuuch

[@HasibUddin-tb8uk]

Best visualization Ihave ever seen...thank u so much sir 😍😍

[@shrivel-vy5kx]

this was seriously such a great help, amazing visuals, thanks for posting such helpful content!

[@sciencetechnician8787]

Amazing explaination !! Really fond of such videos , need more and more videos on such interesting concepts...

[@IntegrationEnthusiast]

Thank you Sir for your animatical explanation. It seems pretty easy.

[@user-zh7pu9kk6j]

bro this is what I was looking for, spent hours trying to self simulate and understand what each integral does. Thanks. keep making such videos about other topics also. IMPORTANT: also please tell which tool/graph calculator are you using.

[@lux-nocopyrightmusic]

Best video on this topic!!! Finally got it:)

[@georgesadler7830]

Thank you for the video/lecture on How to Set Up Double Integrals in Calculus Three.

[@benarkonovich4581]

yk you dont have to capitalize every word right

[@only1tiberious]

Very helpful, I've never taken calculus or anything above algebra yet, but this definitley expanded my knowledge on how these work.

[@BrodieMitch]

must be decent at geometry though

[@pseudovictim]

Brilliantly explained! Thank you!

[@big_creamo]

Phenomenal video for conceptual understanding

[@wafialfaruqhi6860]

you deserve more views great content

[@punditgi]

Beautiful description! Well done. Makes it clear as a bell. 😃

[@chetankadiwal2259]

So satisfied being Engineering student Ton of thanks

[@rajeewprasath7879]

The best explanation ..🤟

[@atulverma3033]

Desperately searching for this video ❤

[@storminmormin14]

This was fantastic. Thank you so much!

[@kikou_]

Very well visualized!

[@user-wq4yl9nb9z]

The best visualization. thank you ❤

[@yashsingh6508]

Amazing visuals!

[@tangpiseth8416]

This is great!

[@alifardanqureshi2969]

how did they manage to describe something so complex in a complex way and still made it not look so complex HAHAHAHAHAAH

[@chrisduo1098]

what is the best video to let us understand the topic easily

[@ryansafta8800]

Most beuatiful video ever, thanks you

[@AJ-et3vf]

Great video. Thank you

[@jonathanpopham5483]

Great video!

[@Tarifkhan-kd9px]

Thank you🙏

[@user-mr5cm7yh6h]

Thinks so much I was so interesting teaching. Unfortunately in Afghanistan it will be so hard to we know about that. That's your help with us. Best regards...

[@kuba2344]

Thank you so much

[@GulzarAhmad-sw1kh]

Excellent

[@user-ny6gw9sv6i]

love you, so helpful!!!

[@darklordyt5980]

lovely video🥰

[@salsalazar7646]

This is awesome😮🎉

[@atulverma3033]

Incredible 👍

[@RogasTV]

Yes! Thank you for the explanation. It has finally clicked. The key information for me is that the inner integral returns a function, not a value, like a single integral would do. So the inner integral contains the information about the curvature. It’s like function currying in programming. That’s a like a and a sub :)

[@jayp9158]

Yes, that was my fav part of the video as well. The other videos never bother to explain the integral's bounds.

[@krumpy8259]

Thank you for the video. My questions: 1. what is the function for that red solid at 1:20? 2. what would the function be if the rectangular part of that red solid had been parabola shaped as well?

[@wanmanchannel189]

What program did you create?

[@benzene979]

thankyou very much

[@tonystark6150]

Thank you❤🌹🙏

[@riflesightsonme2120]

Amazing

[@omerkarhan5625]

perfect

[@alvarosanchez5090]

thank you!!!!

[@prashantkumar8045]

Nice

[@Mahm00dM0hanad]

I can not thank you enough

[@geektoys370]

The first time you said we determine the variable by the axis perpendicular to the slices ( 1:30) but then when the parabola came you said “ parallel “ [ 2:55] I mean what? Can you explain please

[@Impedance_Z]

I am confused like for the parabola case moving along the x-axis shall only reduce the bound of parabola along y-axis how is it decreasing it's height i am not getting it ??

[@user-hi5fb6xf9t]

How did you get equations for curves??

[@user-ck6vc4bu4j]

what is the interpretation if the outer integrals are also some functions of y

[@paritavaghani]

I want to use this animation to find answer of my questions so how can find it

[@pasupuletimangapathi9680]

What will the g(x,y) do in the equation?

[@TheGuruNetOn]

It's like a for-loop looping across a stack of slices.

[@geektoys370]

first, you say the variable is determined by the axis who is prependiculer to the slices, but in 2:57 you said "parallel" what changed? i didnt understannd the choice of variables

[@bhartigupta8894]

Sir will you please make a video on the animation of this👉 double integral e^(x^2) dxdy in the region 0

[@geektoys370]

In the first example 1:30 what is perpendicular here? Isn’t it A(y)?

[@niom9446]

what is g in the last one though

[@vincentnguyen4204]

This video is goated, why study at ut when a&m be actually teaching

[@vincentnguyen4204]

I am going to drop out of UT today

[@objectoriented3049]

​@@vincentnguyen4204based

[@user-mr5cm7yh6h]

If anyone knows, how we can draw it or in which application we can draw it. Please share with me. All the best...

[@koviddadhich991]

Hey can you make same for triple integrals and if possible other topics that require 3d animation. huge request

[@quandarkumtanglehairs4743]

nnnDope af my dude

[@engineers_hub]

how to do these animations

[@JeanDAVID]

Then what is g(x,y) knowing the bounds are the 2 functions ?

[@itsflow3584]

did you find out cos i got the same question

[@JeanDAVID]

@@itsflow3584 usually g(x) is the difference of the 2 functions and the bounds are the x coordinates of the points where those functions cross !

[@itsflow3584]

@@JeanDAVID haha yep got that too chur

[@phee4174]

2:36 err this is pedantry on my part but there is a formula for the area under a parabola it's a|(r - v)^3|/6 where a is the coefficient of x^2 in the polynomial describing the parabola and r and v are the roots of the polynomial (assuming at least that you're looking for the area between the two parabola between it's two intersection points with the x-axis, if not the formula you get is much less nice), admittedly this formula is gotten from integrating the polynomial at it's 2 roots, but it's a still formula for the area that's much 'nicer' then an integral,

[@jordanthomas9508]

i love you

[@mathyyys8467]

i see it as a for i in range including a for j in range

[@almanduku9043]

😮😮😮

[@duckyoutube6318]

Oh i see. So the first thing we learn is a number line from 0 to 10. Then we learn decimal places in a new number line from 0 to 1 example: 0, 0.1, 0.2, 0.3,....1 Then we learn about negative numbers from -10 to +10 in a new number line. Then we stack 2 number lines so that we have an x line and a y line. Then we introduce imaginary numbers on the left side of the xy lines. Then we describe 2d shapes, objects, motion, ect. Then we take the derivative or the rate of change of a tangent point on the xy plane. Then we can take the area under the curve because we now know the rate of change and can now implement things like the power rule and the chain rule. Then we learn that you can use integrals, limits, and derivatives algebraicly, allowing use of ordinary differential equations. Then we make a new number line so we can describe 3 dimensional objects, and motion. And now we use partial derivatives to describe the rate of change in this 3d curve. We take the derivative of each dimention with respect to a single dimension. And now we use double integrals to describe the area under both curves and use the relationship they have with each other to describe volume. So all i need to do calc is to understand the axioms of algebra, systems of equations, and trig. Add in summation. That doesnt seem so hard. Calc is just new notation same logic as algebra mixed with new definitions and techniques of using both the left hand side and right hand side of graphs/equations.

[@SamsungA04e-dp7kj]

0-0+0 : GPS Water Bambang Tri Hasta

[@geektoys370]

Bro you say different times each minute wtf

[@debilista]

I suck at maths, i picked extended maths for highschool because i couldnt force myself to learn it on my own I wasnt satisfied to i went on for engineering and i must say i hate it even more but now i can do anything I do triple integrals daily but man this visualisation was cool, the only thing it lacked is showing what the values of the function are as the function 'swipes' to visually prove that it moves too and set one at constant rate of change and integrate it to the constant rate, then the other as a constant rate and integrate it that way so that it doesnt matter whether you integrate x, y or whatever in whatever order but it would still work.