surface integral, example 2 (KristaKingMath)

► My Vectors course: www.kristakingmath.com/vector...
In this video we'll learn how to evaluate a surface integral, where the surface is the hemisphere that lies above the xy-plane.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@saltygoose2943]

It’s amazing how each person who teaches this does it a different way.

[@tanjents]

You are the best. The video was super clear and concise!!!

[@danika1425]

Nice explanation, thank you :)

[@davenrai]

Krista, thank you so much for always posting the same problems from the textbook! It helps so so much.

[@kristakingmath]

Glad it could help!

[@tanakachiwara6530]

Which textbook is this?

[@Iris-zr1rf]

@@tanakachiwara6530 Stewart Calculus section 16.7 Question 17

[@MyThundermuffin]

KRISTA ! I LOVE YOU

[@dhimanroy1671]

You are a very good teacher

[@AriyanAghamiri]

Great as always!

[@Neueregel]

good example of multivariable calculus

[@prasanjitsamantaray5902]

I like your voice with very simple and clear explanation 👌

[@jimbookiller]

I love you. Excellent tutorial

[@denizozbek9962]

Helped so much! You are very sweet for posting these videos :)

[@kristakingmath]

I'm so glad it helped!

[@mentorman6285]

You've saved me - thank you so much Wish my lecture can see what it really means to lecture Maths

[@kristakingmath]

+Caiphus Man You're welcome, I'm so glad I could help!

[@pauljohnson3867]

Very lucid explanation

[@kimmy208]

thank you for a great video tutorial, it helps a lot, hope you can do more examples :)

[@kristakingmath]

Thanks!

[@wahidhamidy6886]

that was so helpful miss! i appreciate your effort!

[@kristakingmath]

I'm so glad it helped! :D

[@lucascorleto2389]

Hello, I want to ask what exactly are we calculating? its the surface of the function in the enclosure xx + yy + zz = 4 or it is a volume? hope you can clean this doubt for me. very thanks

[@joydeepdeb2025]

Thank you Maam, Just one question can we do it using Divergence theorem

[@vanillapie8321]

what in the limit determines that it is only the positive half sphere instead of the whole sphere?

[@hollywood1476]

Helpful video

[@neetiverma8988]

ma'am, what if we consider sphere in place of sphere? How will it impact the answer?

[@marcellacella8293]

Clear explanation

[@ashutoshpanigrahy7326]

Thank you so much for the example!

[@kristakingmath]

You're so welcome, Ashutosh! :)

[@amararyan4128]

Made me understand. Thank you very much ma'am.

[@kristakingmath]

Glad it could help!

[@tommywalker1631]

so anytime i can any integral funtion and i see the equation for a circle or cynlinder i automatically and ro start thinkig of the limites being 2pi \0 or pi\0

[@Elliott_Ives]

What if it is bounded by Z ≥ 1? How does that change the problem?

[@kakomamululu8652]

Say our our surface integral double S, has three components I,J and K. Does this method work seeing that this example only contained I and J??

[@AtliTobiasson]

Cool, but what about the bottom flat surface of the hemisphere?

[@nanorbalian6037]

thank you very much your videos are great ! what if we are calculating for a portion of a sphere in the first octant ? what would the angle be ??

[@unfeickmas9960]

hello, I think It would tetha from 0 to pi/2

[@unfeickmas9960]

It would be

[@victorcamara2155]

You made this understandable but it's still so complicated 😭😭

[@EricPham-ui6bt]

We may be better off put the z component in the trigonometric form of component x = r cos theta and y = r sine theta then derivative may be found

[@bestsetpantakul6065]

If I do it with plane z=1 it would be the same?

[@moustaphayoussoufissa544]

Thanks so much. Isn't for the spherical coordinates we have phi ? You just consider theta and r . I really appreciate if you make this point clear for me?

[@vanillapie8321]

same question, what about phi?

[@exploringnaturalbeauty2102]

Thank you mam..love from india

[@ankeshpatel523]

awesome

[@taimur1050]

How would we do the same integral over the whole sphere rather than just the top half?

[@kristakingmath]

Since the sphere is symmetrical, you could just do the top half like we did, and then double your total in order to get total volume for the whole sphere. Or, you could change the bounds on the integrals.

[@barshapal3229]

What if sphere is off centre?

[@jmmanda1234]

What if you do not want to change your equation to polar coordinates? Can you still stipulate D and solve this surface integral?

[@kristakingmath]

+jmmanda1234 Yes, you don't always have to change to polar, it's just that sometimes it's easier to change to polar, which is why I did it here.

[@meep6188]

i'll stipulate the D for you

[@kiennnguyen1842]

Can we use spherical coordinates to evaluate this integral ???

[@nikolaiguzman6142]

I have the same question :(

[@agpiccolo]

Sure. Keep rho=2 and integrate phi from 0 to pi/2 and theta from 0 to two pi. I got the same answer.

[@steventhangcem125]

you are an amazing.

[@kristakingmath]

I'm glad I can help. :)

[@engineerhere1061]

U r awesome thank you so much dear love you

[@scottsmith4778]

is this Surface integrals of scalar functions or vector field??

[@moipnou]

scalar

[@salvationude-natha398]

what coordinates is this? Spherical or cylindrical?

[@kristakingmath]

Spherical 👍

[@lenapaulsstepbrother2338]

The fucking GOAT.

[@xiii1818]

Why Zx = -x/z ? It should be: -2x ?

[@JKhal]

factored it down 2z = -2x 2's cancel leaving -x/z

[@vivekvarasada2806]

F = [5x³, 5y³, 5z³], S: x² + y² + z² = 4 surface integral by gauss thm im getting ans 640 times pi but book says ans is 384 times pi can anybody help me out🥲

[@pratyushkumarrout9781]

Sweet voice

[@margaretbelanger2537]

i love you. i want to make you a cake. thank you haha

[@studymode5899]

Aint it shud be 0 to pie instead of 2pie?

[@michaelkindle3391]

no, remember, you are integrating with respect to the whole upper hemisphere. which is still 360 degrees. you are in R3. Remember, the upper half of the sphere has a trace of a circle, and a circle is from 0 to 2pi. You are thinking in terms of going from x=2 to x=-2 when in fact if you look at the graph, you are going from x=2 to x=2, which per the unit circle, translates to the angle of 0 to 2pi.

[@igorfritz2973]

no

[@vanillapie8321]

@@michaelkindle3391 what in the limit determines that it is only the positive half sphere instead of the whole sphere?