Evaluating a Surface Integral - Basic Example

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Evaluating a Surface Integral - Basic Example.
In this video, I do one example of evaluating a basic surface integral.

[@patrickjmt]

Hi Reddit from P4trick_JMT! Thanks for the kind words and good luck :)

[@miladmzz]

No comments only that you are a life saver ... You have said my ass for times throughout the college .. 1st, 2nd, 3rd and 4th year of engineering school ... Thanks man I wish instead of paying tuition fees to my shitty college I could give it all to you !

[@kariina119]

Thank you! You should do a video of flux.

[@robtaylor5769]

Yas

[@gourmetpro6784]

you basically have saved me 5000 dollars of retaking this course, you are better than all profs around the world,

[@lagoonroom4600]

You are seriously the best

[@patrickjmt]

Thanks ;)

[@khalidabuelnaser526]

+Selina Cox yes indeed , Patrick Videos gives us the hope understanding Maths..Big Thanks to the legend #PatrickJMT

[@s0812034]

can u make a video talking about the stoke's theorem?

[@adityavarma193]

I would be stoked for that video. Where is the door again?

[@sravssharma8795]

do a video for stoke's theorem as well plzz

[@CrushOfSiel]

Thanks Patrick! After watching your videos NUMEROUS times, and putting in lots of effort. I think I finally can do most surface integrals I'll come across (scalar, vector, parametrized surface) definitely one of the more tougher subjects in a multivariable course.

[@Halfblackninja92]

I love how half the video is just evaluating the integral, like 90% of calculus is evaluating the integral and 10% of different cases. Thanks Patrick I

[@capcomcrazyl4]

You sir are a gentlemen and a scholar. Thanks for making all of this easy to understand!

[@KentHawkings]

@Bleachnarutoawesome It really isn't. Once you have a good understanding of single integration doing multiple integrals of any form are not THAT difficult once you see what you are actually evaluating (using Riemann sums)

[@propea6940]

Shouldn't the upper bound on y be (2 - 2x/3)? Since we are integrating over the triangle and not the rectangle? It seems here that just using 2 as the upper bound on y makes this problem an integral over a rectangle.

[@MrAAMNNITAllahabad]

Mr. Patrick thank you for video. I've a question for you; please tell how ds = (1 + fx^2 + fy^2)^(1/2) come?? Please let me know, I'd be grateful to you.

[@nikan4now]

Thanks. Could you do an example of surface integrals where the surface's projection is not a surface, like a standing cylinder?

[@varunnanjundarao8139]

Could you please explain the physical significance of surface integrals

[@tylermclellan4954]

It tells you the surface area of an object. That is it tells you the summation of the area of each face of an object. Think if you wanted to gift wrap something as efficiently as possible. That is you wanted to use as little wrapping paper as possible. The surface area would tell you how much gift wrap you needed for any object and the surface integral will tell you how to find the surface area.

[@DaNormalMan]

he actually does cube the three, but he then divides by three (10/3).

[@chadblumenshein5560]

Really awesome videos. You go to a depth of detail that a lot of professors tend to miss. If you have the time could you do videos on calculating flu through a surface.

[@euniceansah6320]

Please help me solve this Evaluate the surface integral where s is the portion of the graph of the function bounded below by x and y

[@aerowenn]

@metaserve You sure did, 16.7 problem #5. Setup on these are the only thing that can get hairy, solving a double integral is old news.

[@pretzels713]

somebody give me a real life example in which this stuff will be used (other than math professors and mathematicians, duh)

[@kluxaveli]

Patrick Rulez KZbin!

[@zhbarton]

@Bleachnarutoawesome No they aren't bad at all once you understand multiple integration.

[@tejasgoyal9590]

please explain where the square root term came from? analytical proof would be highly acknowledged.. thanks

[@mathematicandlogicexplorer8632]

It is the arc length formula, I've seen the same thing in Line integrals.

[@andrewa9064]

Tejas Goyal you to take the magnitude of the Normal vector of the plane since it's an Integral going over a smooth plain. Similar to a line integral

[@philbert_io]

his vids are the best math vids much better than any of the mit open learning stuff

[@lisaodland8452]

I'm trying to help my son with his geometry and this is still totally non-understandable. Picture math and I do NOT get along!

[@davidkipp9259]

I don’t think this is supposed to help with geometry lol

[@matmania1]

@pretzels713 to give maxwell equations of your cell phone?

[@1schwererziehbar1]

I came here from Le Reddit *tips fedora*

[@patrickjmt]

+I lol, nice! Hi Reddit!

[@1schwererziehbar1]

This is the post: www.reddit.com/r/EngineeringStudents/comments/5gletv/its_that_time_of_year_again/

[@aaronbhatia]

Came here to help understand a practice problem from my textbook, and you're using the EXACT same example. Patrick, I'm convinced you are a saint sent from the highest parts of heaven.

[@thesamklick]

Love the videos! But does anyone else notice that the volume level of his voice seems to fade in and out as he speaks?

[@w4yn6]

hmm.. I am thought a slightly different method though.. In my lecture notes we always find a parametric form for Z and then we integrate. For instance r(u,v) = P(u,v) i + Q(u,v) j + R (u,v) k.. we then find the partial derivative of ru and rv, find its cross product and take its determinant. So i'm kinda confuse here.. so there's more then 1 method to this? please enlighten me.

[@GrrRawrr]

Grant Williams. He was right the way you're doing it would be: (10/3)*(3^3) or 3.333*27=90

[@yllbuzoku1670]

Dude, youre gonna get me into uni! Thanks so much.

[@ShadowNinjaIceWolf]

You need this to get in?!? Most people don't see this until their second or third year of it.

[@ShinobiLifeOnline]

ShadowNinjaIceWolf Try Calc 1 2 and 3 in one semester.

[@xShadzHD]

I'm seeing it in first year of uni

[@alexweeda2826]

i didn't get the distribution step. Sorry could you explain that bit, i get the rest of the video

[@GymRat1013]

Very nice video, there is an error in it though. At 6:27, when you integrate with respect to 'x', you square the 3 that should be cubed. I think it comes out to 155*14^1/2.

[@hh6427]

I don't know why, but for some reason none of the sound in any of your videos is working for me

[@1sidsly]

dS is the surface element you are integrating over, and Z is the third dimensional co-ordinate axis. e.g a cube of volume 1 would have a corner at x,y,z =(1,1,1)

[@rockfootballdude]

U ARE A FUCKIN LEGEND...... i guess i can proceed to getting my university degree now, take that mechanical engineering

[@woongbin218]

what if we are given an equation of a cylinder, how can we find the bound? :(

[@invine15cible]

@pretzels713 its incredibly useful if you're in electrical engineering and you have to take an electromagnetic fields class.

[@VeXorian1337]

@kbkrisp Automatic sound gain adjustment to avoid distortion. A lot of software/hardware posses this feature.

[@adeyemiadesuyi8388]

From grateful heart her.. am every pleased with the example sir'

[@swipenet]

nope, it was 3 cubed times 10/3 and he simply made that 3 squared times 10 which is 9 times 10 = 90.

[@lightmarepeno]

This video is good but you being left handed really ruins my concentration. Can you switch to right handed?

[@jdith01]

i havent even had to do this stuff yet but i probably will this year so thanks in advance haha

[@djveneko]

does anybody know a good video it could be from Patrick or from some one else that explains how you get the limits when all they give you is the plane and the boundaries... if im making any sense it makes sense in my head cause i know what i wan and need but dont know if it makes sense for you guys ... thank you in advance...

[@TheOhmansam]

This is problem 5 out of chapter 16.7 of Stewart's 6th edition of calculus....

[@abdullah57habib]

@noon0788 I think you meant *stupid..Irony at its best.. Patrick is awesome!

[@marcthompson5633]

These videos are great!!! just in case you ever read this, the 90 should be a 30, (10/3) times 9 equals 30

[@durbansurfmadness]

so i got my engineering maths exam next thursday, and patrick, you're a flipin boss. I'm thinking about giving you my first paycheck. I'l keep you posted!

[@blackconfucius4974]

Yuri how did college go?

[@GymRat1013]

Sorry, you canceled out a 3, my mistake. It is 1am.

[@Zeppelinpuppy]

PatrickJMT for the win!

[@legendarysannin65]

how do i find out the limits of the integration?

[@connorjones4778]

You forgot to divide by the 90 by 3 at the end but good video apart from that thanks.

[@showmikalam8608]

after dividing by 3 we get 90

[@pretzels713]

@invine15cible thanks, im gonna be doing that.

[@khalid97899789]

patrick = boss of youtube

[@sabangtissamaef.7126]

Thank you

[@liquidstl]

calculating the flux of an electric field

[@casjede3267]

it would be best if you can link your follow ups videos cuz i ve been struggling to find them q.q but thank you very much for the hard work !

[@MrQwerty123627]

Did you find them

[@tylerdurden786]

ff ds did you?

[@trudal987]

Could you do a flux integral problem??

[@syabongajele6431]

thanks

[@meestroo]

Tomorrow is the day!

[@ClaraLi94]

YOU ARE AMAZING PATRICK :D

[@pretzels713]

eh?

[@Pimphats]

i luv you, dont stop doing what you do

[@najeehull4549]

Patrick you are the man

[@johnsmith-ro8mt]

You are lefty 😊

[@kavikavi1534]

Thank you sir.🙏

[@patrickjmt]

Most welcome

[@Ronaldoo91]

what if there wasnt a z

[@reiallester848]

Nice Video

[@gellybelly2]

Awesome explanation Pat :D

[@ismailhurmek7846]

go patrick

[@DSnyd901]

great work

[@KanitaKhaled5]

I love you Patrick!!!!

[@ura239]

NICELY EXPLAINED BRO!

[@tanayagar]

Thank you!!

[@sparksfly44]

Thank you!

[@Yachao23]

Hey Partrick, I just wanna say thank you for all of your videos. They helped me tremendously over this Spring semester; as a result, i got an A from my Calculus 2 class!! I am certainly going to make a donation. Please keep up the great work, you're the best!!

[@atulnamdev7546]

Excellent,well explained

[@patrickjmt]

thanks