Double integrals to find surface area (KristaKingMath)

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  • Опубліковано 2 лис 2024

КОМЕНТАРІ • 162

  • @annaecn
    @annaecn 4 роки тому +20

    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
      @kristakingmath  4 роки тому +3

      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
      @splendidteaching 3 роки тому

      Yes, I second Anna's comments :-)

  • @YSCOTTY
    @YSCOTTY 11 років тому +2

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

  • @ottoomen5076
    @ottoomen5076 7 років тому

    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.

  • @splendidteaching
    @splendidteaching 3 роки тому +1

    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
      @kristakingmath  2 роки тому +1

      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! :)

  • @Gab8riel
    @Gab8riel 8 років тому +13

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

    • @kristakingmath
      @kristakingmath  8 років тому +8

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

  • @muwongeevanspaul9166
    @muwongeevanspaul9166 2 роки тому

    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.

  • @muwongeevanspaul9166
    @muwongeevanspaul9166 2 роки тому

    And to be Honest, since my year 1,i have depended on your UA-cam 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.

  • @T-Rex_7
    @T-Rex_7 7 років тому +1

    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

  • @9999Mrgold
    @9999Mrgold 10 років тому +3

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

    • @kristakingmath
      @kristakingmath  10 років тому +2

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

  • @VictorMusara
    @VictorMusara 8 років тому

    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
      @kristakingmath  8 років тому +1

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

  • @KillianDefaoite
    @KillianDefaoite 6 років тому

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

  • @Abdoolkasim
    @Abdoolkasim 7 років тому +2

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

  • @folsomboy86tbone15
    @folsomboy86tbone15 Рік тому

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

  • @danielvanbibber991
    @danielvanbibber991 4 роки тому +3

    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
      @kristakingmath  4 роки тому +1

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

  • @DIPNILIMDAS
    @DIPNILIMDAS 7 років тому

    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

  • @LedgerLines000
    @LedgerLines000 11 років тому +1

    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

  • @monukumarthakur3068
    @monukumarthakur3068 6 років тому

    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

  • @kristakingmath
    @kristakingmath  11 років тому +2

    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
    @WishedForWishes 8 років тому +1

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

    • @kristakingmath
      @kristakingmath  8 років тому

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

  • @jimexsha
    @jimexsha 6 років тому

    you are very good at giving explanation

  • @titeenum
    @titeenum 3 роки тому

    thank u Krista , it helped me a lot

    • @kristakingmath
      @kristakingmath  3 роки тому

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

  •  11 років тому

    You are really good, congratulations on your work!

  • @maximumx5
    @maximumx5 10 років тому +4

    Love the explanation of this, thank you :)

  • @kristakingmath
    @kristakingmath  11 років тому

    So glad I could help! :)

  • @andrewobrigewitsh
    @andrewobrigewitsh 9 років тому +1

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

    • @kristakingmath
      @kristakingmath  9 років тому +2

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

  • @ChristopherCTech
    @ChristopherCTech 11 років тому

    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!

  • @md65000
    @md65000 9 років тому

    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
    @kristakingmath  11 років тому

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

  • @ThePinoyMamba
    @ThePinoyMamba 11 років тому

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

  • @KhabisangLekena
    @KhabisangLekena 9 років тому

    Nice presentation, um gonna chow this now.

  • @TechWiseforSeniors
    @TechWiseforSeniors 9 років тому

    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

  • @nadra963
    @nadra963 9 років тому +1

    THANK YOU SO MUCH. you saved my test paper!

  • @Rayquesto
    @Rayquesto 11 років тому

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

  • @clearmathsconcepts9531
    @clearmathsconcepts9531 2 роки тому

    Excellent video

  • @cesarmelendez2577
    @cesarmelendez2577 3 роки тому

    Amazing video. Blown away.

  • @Him2814u
    @Him2814u 2 роки тому

    Thank you much!

  • @sfundoy5dube59
    @sfundoy5dube59 3 роки тому

    well explained thank you

  • @TheAuroraborealis7
    @TheAuroraborealis7 2 роки тому

    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

  • @ChefFarisMom3
    @ChefFarisMom3 10 місяців тому

    Thank you so much

  • @kristakingmath
    @kristakingmath  11 років тому +1

    Thank you so much! :D

  • @mibrahim60
    @mibrahim60 6 років тому +1

    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
      @jessewest5456 3 роки тому +1

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

    • @mibrahim60
      @mibrahim60 3 роки тому

      @@jessewest5456 Thank you ,I graduated 3 years back

  • @raushankumarpathak8939
    @raushankumarpathak8939 2 роки тому

    Thanks

  • @amattamana
    @amattamana 4 роки тому

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

  • @АйдарАзизов-ч7б
    @АйдарАзизов-ч7б 3 роки тому

    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

  • @EricaLuvsYella
    @EricaLuvsYella 5 років тому

    Thank you so much!!

  • @amonevelina8261
    @amonevelina8261 10 років тому

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

    • @kristakingmath
      @kristakingmath  10 років тому

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

  • @vedangbale1794
    @vedangbale1794 2 роки тому

    Thank u for this video 🤗😺

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @allstarshotta
    @allstarshotta 10 років тому +1

    Smart & beautiful. Thank you👍

  • @Anonymous-rt7gh
    @Anonymous-rt7gh 5 років тому

    Thank you mam. You are great.

  • @NirajHirachan
    @NirajHirachan 11 років тому +1

    thank u :)

  • @TheDanischannel
    @TheDanischannel 8 років тому

    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
      @kristakingmath  8 років тому

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

  • @Orange_Juice796
    @Orange_Juice796 8 років тому +4

    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
      @kristakingmath  8 років тому +2

      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
      @computerdude65 5 років тому

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

  • @yhs3323
    @yhs3323 9 років тому +1

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

  • @azharhaseeb5064
    @azharhaseeb5064 8 років тому

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

  • @LizardanNet
    @LizardanNet 11 років тому +17

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

    • @kristakingmath
      @kristakingmath  11 років тому +6

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

    • @Bladermishal10
      @Bladermishal10 4 роки тому

      Damn thanks I was wondering about that

  • @hourtbora3072
    @hourtbora3072 9 років тому

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

  • @VinothKumar-qo7ry
    @VinothKumar-qo7ry 7 років тому

    Thank u so much

  • @kristakingmath
    @kristakingmath  11 років тому

    Thanks! :)

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @homebodytiger
    @homebodytiger 7 років тому

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

  • @PEACEFU
    @PEACEFU 10 років тому +1

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

    • @KabooM1067
      @KabooM1067 10 років тому +5

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

  • @zakariyajabri
    @zakariyajabri 8 років тому

    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
      @kristakingmath  8 років тому

      +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.

  • @FRAESMRAOSD
    @FRAESMRAOSD 11 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    you're welcome!! :D

  • @parkerd2154
    @parkerd2154 7 років тому

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

    • @parkerd2154
      @parkerd2154 7 років тому

      Assuming 2pi*radius was included in the integral

  • @JeanDAVID
    @JeanDAVID 11 років тому

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

  • @amrhetler007
    @amrhetler007 11 років тому

    very Helpful. Thank U. :)

  • @estherkim182
    @estherkim182 10 років тому +2

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

    • @pupper6044
      @pupper6044 10 років тому

      Noticed it too bro.

    • @teslacarfan
      @teslacarfan 9 років тому

      I think you're right. I noticed it.

    • @Wing0fSilver
      @Wing0fSilver 9 років тому +2

      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 :)

  • @sleighbeggy6250
    @sleighbeggy6250 6 років тому

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

  • @AyushSingh-hq4jd
    @AyushSingh-hq4jd 6 років тому

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

    • @kristakingmath
      @kristakingmath  5 років тому +1

      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
      @AyushSingh-hq4jd 5 років тому

      @@kristakingmath thanks for clarification mam😊

  • @YernagulaHemanthRamaKrishna
    @YernagulaHemanthRamaKrishna 8 років тому

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

  • @oukphonnarith524
    @oukphonnarith524 8 років тому

    thank you
    i like your video

    • @kristakingmath
      @kristakingmath  8 років тому

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

  • @yoyocharms2350
    @yoyocharms2350 6 років тому

    Thanksss

  • @BrandonWinning41
    @BrandonWinning41 9 років тому

    So much easier to use polar integration on this problem.

  • @naborpalomera8642
    @naborpalomera8642 8 років тому

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

    • @kristakingmath
      @kristakingmath  8 років тому

      +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.

  • @edmondmalepane3141
    @edmondmalepane3141 5 років тому

    you the best

  • @jamesmcloughlin776
    @jamesmcloughlin776 4 місяці тому

    Why is r included with dr dtheta

  • @tanwarsingh396
    @tanwarsingh396 3 роки тому

    Nice 👍

  • @MohammedAli-lw7kk
    @MohammedAli-lw7kk 10 років тому

    u are good

  • @mycelleismybffl
    @mycelleismybffl 11 років тому

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

  • @nicolenelson9180
    @nicolenelson9180 8 років тому +1

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

    • @joshuajardenil3661
      @joshuajardenil3661 8 років тому +2

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

    • @nicolenelson9180
      @nicolenelson9180 8 років тому

      oh ok, Thanks!

  • @aliilyasmohamed1193
    @aliilyasmohamed1193 4 роки тому

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

  • @keerangovender1179
    @keerangovender1179 9 років тому

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

    • @LeinysandMassey4life
      @LeinysandMassey4life 9 років тому +3

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

  • @hamsack981
    @hamsack981 7 років тому

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

    • @kristakingmath
      @kristakingmath  7 років тому +1

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

    • @hamsack981
      @hamsack981 7 років тому

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

  • @mrdalzd750
    @mrdalzd750 5 місяців тому

    you forgot to substitute limits of integration after u substitution

    • @kristakingmath
      @kristakingmath  5 місяців тому

      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. 🤓👍

  • @diegoelizondo1991
    @diegoelizondo1991 5 років тому

    i looooove you, thanks

  • @hg2.
    @hg2. 7 років тому

    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
      @mcawesome4150 7 років тому

      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
    @forhadhasan3891 2 роки тому

    I love youuuu.

  • @asmcriminaL
    @asmcriminaL 10 років тому

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

    • @andrewmorehead3704
      @andrewmorehead3704 4 роки тому

      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.

  • @jenskrarup5407
    @jenskrarup5407 4 роки тому

    espectacular

  • @MahmudulHasan-fn5lk
    @MahmudulHasan-fn5lk 10 років тому

    why dydx = rdrd(theta) ???

    • @MrNightslash
      @MrNightslash 9 років тому

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

  • @MultiChrisjb
    @MultiChrisjb 9 років тому

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

    • @Captain_Jack514
      @Captain_Jack514 8 років тому

      +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

  • @edmondmalepane3141
    @edmondmalepane3141 5 років тому

    can you pleas shar other examples

  • @faheemsatti5448
    @faheemsatti5448 3 роки тому +1

    Who seen this video 2021?

  •  9 років тому

    ı love you.......

  • @KuldeepSingh-wo4yl
    @KuldeepSingh-wo4yl 6 років тому

    👍👍

  • @muchacamara
    @muchacamara 8 років тому +34

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

    • @rileystewart9165
      @rileystewart9165 8 років тому +5

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

    • @rileystewart9165
      @rileystewart9165 8 років тому +1

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

    • @R77456
      @R77456 8 років тому

      +shawn smith Wow, learn to spell you fucking idiot

    • @muchacamara
      @muchacamara 8 років тому

      sob

    • @muchacamara
      @muchacamara 8 років тому

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

  • @cattyperri1174
    @cattyperri1174 9 років тому

    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
    @capitansparrow9952 4 роки тому

    Do you have a E-mail ID?