Evaluating a Surface Integral - Basic Example

In this video, I do one example of evaluating a basic surface integral.

[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 ! 

[gourmetpro]

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

[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.

[kariina]

Thank you! You should do a video of flux.

[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.

[Halfblackninja]

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 <3 U always and forever

[patrickjmt]

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

[capcomcrazyl]

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

[chadblumenshein]

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.

[philbert_io]

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

[s]

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

[sravssharma]

do a video for stoke's theorem as well plzz

[GymRat]

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.

[Yachao]

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!!

[adeyemiadesuyi]

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

[yllbuzoku]

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

[Pimphats]

i luv you, dont stop doing what you do

[nikannow]

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

[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.

[sidsly]

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)