Double integrals to find surface area (KristaKingMath)

► My Multiple Integrals course: www.kristaking...
Learn how to use double integrals to find the surface area.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
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.kristakingm...
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[@annaecn]

Since education has been moved online, my math professor has just been posting links to youtube math lectures. Of these youtube math lectures, your videos are by far the best quality. You work through the problems at a reasonable pace for note taking, you choose problems that are simple enough to emphasize the concepts and not grind ugly algebra, and you have beautiful and legible handwriting.

[@kristakingmath]

Thank you so much, Anna! I'm so glad the videos are helping! :) I know school has been so disrupted for everybody... I hope you're hanging in there and staying safe and healthy!

[@splendidteaching]

Yes, I second Anna's comments :-)

[@splendidteaching]

Well done Krista! Excellent math video. Best I have seen actually. Your audio is clear, good pace of speaking, no um's and err's. Curious as to what software you are using. I use to teach math and have seen some terrible online lectures at university. Be great if they would impliment the tools you are using. I like the touch of your signature in the bottom right corner too. And rightly so....it is a work of art you are creating!

[@kristakingmath]

Thank you so much, Roy, I'm honored!! I'm so glad you like the videos. I use Sketchbook Pro for the "blackboard" software, and a Wacom pen tablet to write. I'd highly recommend both! :)

[@ottoomen5076]

This is your best video! Its contains numerous essential portions of calculus and it explains the most critical parts of solving double integral surface area problems.

[@Gab8riel]

I was about to give up on this subject, thank you

[@kristakingmath]

You're welcome, I'm glad you decided not to give up!

[@muwongeevanspaul9166]

And to be Honest, since my year 1,i have depended on your KZbin videos and other great tutors like u and I have excelled in my maths course units. Am blessed. I just wish I get to see you physically. U are a great mentor,influencer and life inspirer. Your maths is fully anointed of the Lord most high.

[@YSCOTTY]

Beautiful video! Shows how awesome calculus can be without showing it off as threatening. Great work!

[@danielvanbibber991]

Well made, easy to understand video! I'm glad channels like these exist while the coronavirus has cancelled all school until the rest of the year!

[@kristakingmath]

Hang in there, Daniel! I hope you and your family are all safe and healthy! :)

[@VictorMusara]

Today I had one of the moments I get stuck while writing an assignment that is almost overdue...and then Krista King comes and saves me. THANK YOU.

[@kristakingmath]

+Victor Musara You're welcome, I'm happy to help!

[@T-Rex_7]

I love you. You won my heart. I was dealing with this problem for 30 minutes and then I found your video and then Your cute voice solved my problem

[@muwongeevanspaul9166]

I just Love your maths Lady Krista. 👍👍👍👍👍 I just love it. There is no number u have ever explained and I dint get it. Thank you so much,really much. Am blessed to have gone thru your gifted hands as well.

[@9999Mrgold]

This is well explained. Thank you for your free help.

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@kristakingmath]

WOW, that's awesome!! Good for you for doing the double degree in Economics and Mathematics! That's going to be a lot of work, but it'll definitely pay off! Keep up the great work!! :D

[@WishedForWishes]

Thank you for the "reminder" part at the beginning of your video, I completely forgot about the formula regarding surface area.

[@kristakingmath]

+Ranjot Gill You're welcome, I'm glad it helped!

[@KillianDefaoite]

This was EXACTLY what I was looking for. You have my utmost gratitude.

[@Abdoolkasim]

Thanks for sharing your mathematical knowledge with your beautiful explanations.!

[@LedgerLines000]

have you ever worked as a tutor? by the time most people get to calculus, they become thrifty and sloppy with their algebra and arithmetic, usually to their detriment. I love your methodical approach, taking nothing for granted, willing to rewrite equations with each adjustment. it reminds me of what I do when I tutor students, and what I always urge them to do. and as others have pointed out, you have a very calming voice, which is also great for math tutors. keep it up I love what you're doing

[@folsomboy86tbone15]

Really appreciate the nice diagrams and very readable handwriting! If only my students were getting the same out of me. I'm trying.

[@DIPNILIMDAS]

Your Videos are really helpful maa'm. The things that seems to be a nightmare in the class becomes very interesting after watching your video. Thank You

[@kristakingmath]

So glad I could help! :)

[@monukumarthakur3068]

Thank u very much ....Today is our examination of first semm and I did not know how to solve surface area by double integration methode ....So thank u

[@maximumx5]

Love the explanation of this, thank you :)

[@titeenum]

thank u Krista , it helped me a lot

[@kristakingmath]

You're welcome, Ryan, I'm so so glad that the video made sense! :D

[@nadra963]

THANK YOU SO MUCH. you saved my test paper!

[@md65000]

This is a very nice clear explanation of doing the computation but I was really hoping for an explanation of why that formula is what it is.

[@kristakingmath]

Yup! Tutoring is my background. :D Thanks for the comment!

[@ChristopherCTech]

This is a great video, it answered my question completely. I did notice one minor mistake: at 5:31 you omit part of a formula. You should have said, x=rcos(theta), y=rsin(theta) In this case r=1, but you should probably still point that out. Otherwise, great video. Very helpful!

[@kristakingmath]

Thank you so much! :D

[@andrewobrigewitsh]

Great videos, I've been using them since Calculus 1.

[@kristakingmath]

Andrew Obrigewitsch That's so awesome! I'm so glad I've been able to help along the way!

[@Orange_Juice796]

at 7:55 when you make the u substitution, is it not necessary to change the limits of integration on the first integral? Thanks

[@kristakingmath]

I should have changed them, but I back-substituted later in the video, which means that I would have changed the limits back to the original ones, anyway.

[@computerdude65]

not when you substitute the function back in for 'u'

[@ThePinoyMamba]

Wow. Thanks Krista You definitely Rock!!! Your awesome!

[@TheAndroidDictator]

I understand the example that you did. And it was done terrifically by the way. But I'm stuck on this problem where I have to find the area of the surface. The problem is find the part of the plane 3x+2y+z=6 that lies in the first octant

[@Rayquesto]

This is amautar! I want videos on obtaining areas of surfaces in three dimensions which require surface integration. I suggested the hardcord vector calculus!

[@jimexsha]

you are very good at giving explanation

[@mibrahim60]

I love your videos , thank you very much . I have a question here ,when you substituted 1+r^2 by u , did you change the limits accordingly? r=0 then u=1 , and when r =1 u=2 or am I missing something?

[@jessewest5456]

i know its 3 years late but she substitutes r back into the integrand before evaluating the definite integral

[@mibrahim60]

@@jessewest5456 Thank you ,I graduated 3 years back

[@cesarmelendez2577]

Amazing video. Blown away.

[@kristakingmath]

Thank you so much, Cesar! :)

[@TheAuroraborealis7]

don’t you need to change the limits (0,1) after substitution? since u=1 + r^2 you need to also substitute the limits for r=0 you have u=1 and for r=1 you have u=2

[@LizardanNet]

Wrong. X =r cos theta, Y = r sin theta

[@kristakingmath]

Whoops! Thanks for letting me know. Annotated. :)

[@Bladermishal10]

Damn thanks I was wondering about that

You are really good, congratulations on your work!

[@ChefFarisMom3]

Thank you so much

[@clearmathsconcepts9531]

Excellent video

[@kristakingmath]

So glad it was helpful, and thanks for pointing that out to me! I was a little lazy there! :)

[@Him2814u]

Thank you much!

[@allstarshotta]

Smart & beautiful. Thank you👍

[@user-em4dd8sx4y]

Hey Krista King! I love your videos, thank you so much for them, but may you explain please, why do you use that formula. I think that if we want to find an area, we just integrate 1 for dxdy

[@yhs3323]

Why doesnt the bounds change when you implented integral by parts?

[@KhabisangLekena]

Nice presentation, um gonna chow this now.

[@amattamana]

What the r boundary changes to 0-1 instead of -1-1. We are talking about the whole circle, correct?

[@sfundoy5dube59]

well explained thank you

[@kristakingmath]

Thanks, sfundo, you're welcome! :)

[@NirajHirachan]

thank u :)

[@EricaLuvsYella]

Thank you so much!!

[@kristakingmath]

You're welcome, Erica! :)

[@PEACEFU]

I got an question that drives me crazy . Why we can't take -1 to 1 limt for Y also??

[@KabooM1067]

If you do that it will be defining a square instead of a circle.

[@vedangbale1794]

Thank u for this video 🤗😺

[@homebodytiger]

how do you find the surface integral of a circle where z=0 where x>0 and y

[@azharhaseeb5064]

Mam krista.your vidios help many but please tell m e where we can use it in a practical application. .

[@estherkim182]

Don't the limits of integration change from 0-1 to 1-2 once you convert r it into u/du?

[@pupper6044]

Noticed it too bro.

[@teslacarfan]

I think you're right. I noticed it.

[@Wing0fSilver]

She kept them 0 to 1 because she intended to back substitute to r. had she kept it in u it would have been 1 to 2, yes :)

[@raushankumarpathak8939]

Thanks

[@TheDanischannel]

Hey Krista. I have an equation which isn't resolved for 'z'. Am I to first separate 'z' and then initiate the procedure to find the surface area?Like I have this: 36z^2=16x^2+9y^2+144.(With center at origin and radius 3)Thank you in advance.

[@kristakingmath]

+Danyal Tariq Yes, I think that's the way I'd try to approach it.

[@amonevelina8261]

Thank you very much for the video. Your video is very helpful.

[@kristakingmath]

You're welcome! I'm so glad it helped! :D

[@JeanDAVID]

Where is the demo of the formula you tagged "reminder " ?

[@zakariyajabri]

why hasn't the limits of integration change after the U-substitution??? shouldn't they be from 1 to 2 since u=1+r^2??

[@kristakingmath]

+Z jabri I already knew I was going to back-substitute at the end of the problem, so I didn't want to bother changing the limits, knowing I was just going to change them back. But yes, normally you would change them to match the variable, and then change them back if you back-substitute, or evaluate over the new interval if you don't back-substitute.

[@kristakingmath]

Thank you! You're always so sweet!! :D

[@sleighbeggy6250]

what if the quation is integrate of r is from 0 to (1_x^2)^1/2 ?

[@kristakingmath]

Thanks! :)

[@YernagulaHemanthRamaKrishna]

How to select the surface (i.e weather xy plane or yz plane or zx plane.

[@mycelleismybffl]

i don't understand how to do this for example a problem like x^2+y^2+z^2=4 and z=1??

[@Anonymous-rt7gh]

Thank you mam. You are great.

[@kristakingmath]

Thanks, MOHD! :)

[@parkerd2154]

Would this double integral method work to find the surface area of a solid bound by two functions rotated around an axis?

[@parkerd2154]

Assuming 2pi*radius was included in the integral

[@hourtbora3072]

good; there is a bit typo x=rcost and y=rsint

[@hamsack981]

Once again you saved my ass this semester. Goddamn Supergirl over here. ☝

[@kristakingmath]

Just so glad the videos have been able to help along the way! 😊

[@hamsack981]

Krista King do you have or will you be making videos for linear algebra?

[@BrandonWinning41]

So much easier to use polar integration on this problem.

[@FRAESMRAOSD]

x = r cos (theta) y = r sin (theta) r was omitted. By chance, these formulas weren't used in the example : )

[@VinothKumar-qo7ry]

Thank u so much

[@jamesmcloughlin776]

Why is r included with dr dtheta

[@nicolenelson9180]

so what do you mean by type 1 region, I'm confused :(

[@joshuajardenil3661]

+nicole nelson Type 1 region means the outside d is dydx. If it was a Type 2 region, it would be dxdy instead.

[@nicolenelson9180]

oh ok, Thanks!

[@amrhetler007]

very Helpful. Thank U. :)

[@naborpalomera8642]

When you do u-substitution don't you have to change the bounds?

[@kristakingmath]

+Nabor Palomera Yes, but I knew that I was going to back-substitute at the end of the problem, so I didn't want to bother changing the bounds, and then changing them back again, when they were going to end up the same as where they started.

[@AyushSingh-hq4jd]

hey, why u have not changed the limits of integral after taking the substitutions plz clarify me!!!!!

[@kristakingmath]

Hey Ayush! I didn't change the limits because I was planning on back-substituting later. Whenever you make a substitution, you can do one of two things. You can either 1) make the substitution, change the limits, integrate, then evaluate over the interval with the changed limits, or you can 2) make the substitution, keep the limits the same, integrate, back-substitute, then evaluate over the interval with the original limits. You're used to the first option, and I did the second option in this video. :)

[@AyushSingh-hq4jd]

@@kristakingmath thanks for clarification mam😊

[@kristakingmath]

you're welcome!! :D

[@yoyocharms2350]

Thanksss

[@keerangovender1179]

Cant this be done with polar co-ordinates as well?

[@LeinysandMassey4life]

+Keeran Govender watch the whole video, then you can comment.

[@edmondmalepane3141]

can you pleas shar other examples

[@mrdalzd750]

you forgot to substitute limits of integration after u substitution

[@kristakingmath]

I actually intended to leave them, because I was intending to back-substitute into x at the end, before evaluating over the limits of integration. 🤓👍

[@tanwarsingh396]

Nice 👍

[@kristakingmath]

Thanks! ✌

[@edmondmalepane3141]

you the best

[@diegoelizondo1991]

i looooove you, thanks

[@asmcriminaL]

been looking for a few hours on "HOW" this formula works, it's hard to understand.

[@andrewmorehead3704]

asmcriminaL 5 years later, but it’s very similar to the arc length for a two dimensional problem. If you conceptually understand that, it will be the same.

[@MohammedAli-lw7kk]

u are good

[@oukphonnarith524]

thank you i like your video

[@kristakingmath]

+ouk phonnarith You're welcome, I'm so glad you liked it!

[@aliilyasmohamed1193]

Thank you 😊 Mdm really u make me happy today. Today I thought it was rock😂it easy

[@kristakingmath]

:)

[@abaundwal]

Your grammar is killing me man.

[@MahmudulHasan-fn5lk]

why dydx = rdrd(theta) ???

[@MrNightslash]

use the general method of co ordinate changing. Take the Jacobian J(x,y/r,theta) it will come

[@MultiChrisjb]

the area of a circle with r =1 is pi -> A = pi*r^2, so this is wrong.

[@Captain_Jack514]

+Chris B We're not looking for the area of the circle. We are looking at the surface area of the function f(x,y) = xy bounded bounded by the circle x^2 + y^2 = 1

[@hg2.]

Awesome! "Oh... THAT'S why they had this "polar coordinates" class in high school that I took, passed, and never heard from again...." Is anyone besides me wondering about high school math education and what that was all about...

[@mcawesome4150]

hettygreene it actually has many other uses. Take a course in signal processing and you will have to apply all of the maths you learned in high school

[@forhadhasan3891]

I love youuuu.

[@muchacamara]

I want to integrate the area of your heart, Crystal.

[@rileystewart9165]

+shawn smith If you can't even spell her name, she may not be interested sean

[@rileystewart9165]

+shawn smith I'm just messing with you haha, gave me a bit of a laugh sorry haha

[@R77456]

+shawn smith Wow, learn to spell you fucking idiot

[@muchacamara]

sob

[@muchacamara]

learn to mind to own business, fucker. Did I spelled that correctly? XD R77456

[@jenskrarup5407]

espectacular

[@faheemsatti5448]

Who seen this video 2021?

[@KuldeepSingh-wo4yl]

👍👍

ı love you.......

[@cattyperri1174]

wow you are so cute and your voice is so sweet thanks for your great videos I fail my all exam because of you haa haa just kidding just opposite thanks for video it helps a lot during revision

[@capitansparrow9952]

Do you have a E-mail ID?