reparametrizing the curve in terms of arc length (KristaKingMath)

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  • Опубліковано 23 гру 2024

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  • @matj1833
    @matj1833 6 років тому +8

    Your videos are excellent. When Sal's voice puts me to sleep I can throw you in the mix and liven back up. Keep up the great work!

  • @accidentalfrenchfries
    @accidentalfrenchfries 6 років тому +12

    I've been trying to understand my textbook's version of this for an hour. This saved me! I loved how you represented t as a function of s.

  • @SneakyZeke
    @SneakyZeke 7 років тому +32

    sweet jesus thank you you much, multi variable calc exam in 2 hours

  • @kathrynhund5925
    @kathrynhund5925 4 роки тому +4

    I read multiple explanations of this that left out pieces of the explanation and only made me more confuse than when I started. This was the first source to actually make it clear what I needed to do. Thank you for the helpful, informative video!

    • @kristakingmath
      @kristakingmath  4 роки тому

      You're welcome, Kathryn, I'm so glad it all made sense! :)

  • @observer4322
    @observer4322 3 роки тому +1

    That is so much easier that I thought. You are so good at hitting all the points, but keeping the video short. Perfect explanation, thanks.

    • @kristakingmath
      @kristakingmath  3 роки тому +1

      Thank you so much, I'm so glad everything made sense! :)

  • @yj29885
    @yj29885 Рік тому

    Wonderfully explained!

  • @Neueregel
    @Neueregel 10 років тому

    Good example. But in order to find an integer reparametrization result , instead of Root(29), one has to find a *sum of three squares that form a perfects square*. The deravatives of 2t,3t,4t, obviously parametrize to 29, a non-perfect square. So, the whole solution for *integer* reparametrization for x,y,z < 30 are :
    1 ^2 + 2 ^2 + 2 ^2 = 3 ^2
    1 ^2 + 4 ^2 + 8 ^2 = 9 ^2
    1 ^2 + 6 ^2 + 18 ^2 = 19 ^2
    1 ^2 + 12 ^2 + 12 ^2 = 17 ^2
    2 ^2 + 3 ^2 + 6 ^2 = 7 ^2
    2 ^2 + 4 ^2 + 4 ^2 = 6 ^2
    2 ^2 + 5 ^2 + 14 ^2 = 15 ^2
    2 ^2 + 6 ^2 + 9 ^2 = 11 ^2
    2 ^2 + 7 ^2 + 26 ^2 = 27 ^2
    2 ^2 + 8 ^2 + 16 ^2 = 18 ^2
    2 ^2 + 10 ^2 + 11 ^2 = 15 ^2
    2 ^2 + 10 ^2 + 25 ^2 = 27 ^2
    2 ^2 + 14 ^2 + 23 ^2 = 27 ^2
    2 ^2 + 24 ^2 + 24 ^2 = 34 ^2
    2 ^2 + 26 ^2 + 29 ^2 = 39 ^2
    3 ^2 + 4 ^2 + 12 ^2 = 13 ^2
    3 ^2 + 6 ^2 + 6 ^2 = 9 ^2
    3 ^2 + 6 ^2 + 22 ^2 = 23 ^2
    3 ^2 + 12 ^2 + 24 ^2 = 27 ^2
    3 ^2 + 14 ^2 + 18 ^2 = 23 ^2
    3 ^2 + 16 ^2 + 24 ^2 = 29 ^2
    3 ^2 + 24 ^2 + 28 ^2 = 37 ^2
    4 ^2 + 4 ^2 + 7 ^2 = 9 ^2
    4 ^2 + 5 ^2 + 20 ^2 = 21 ^2
    4 ^2 + 6 ^2 + 12 ^2 = 14 ^2
    4 ^2 + 8 ^2 + 8 ^2 = 12 ^2
    4 ^2 + 8 ^2 + 19 ^2 = 21 ^2
    4 ^2 + 10 ^2 + 28 ^2 = 30 ^2
    4 ^2 + 12 ^2 + 18 ^2 = 22 ^2
    4 ^2 + 13 ^2 + 16 ^2 = 21 ^2
    4 ^2 + 17 ^2 + 28 ^2 = 33 ^2
    4 ^2 + 20 ^2 + 22 ^2 = 30 ^2
    5 ^2 + 10 ^2 + 10 ^2 = 15 ^2
    6 ^2 + 6 ^2 + 7 ^2 = 11 ^2
    6 ^2 + 6 ^2 + 17 ^2 = 19 ^2
    6 ^2 + 8 ^2 + 24 ^2 = 26 ^2
    6 ^2 + 9 ^2 + 18 ^2 = 21 ^2
    6 ^2 + 10 ^2 + 15 ^2 = 19 ^2
    6 ^2 + 12 ^2 + 12 ^2 = 18 ^2
    6 ^2 + 13 ^2 + 18 ^2 = 23 ^2
    6 ^2 + 14 ^2 + 27 ^2 = 31 ^2
    6 ^2 + 18 ^2 + 27 ^2 = 33 ^2
    6 ^2 + 21 ^2 + 22 ^2 = 31 ^2
    7 ^2 + 14 ^2 + 14 ^2 = 21 ^2
    7 ^2 + 14 ^2 + 22 ^2 = 27 ^2
    7 ^2 + 16 ^2 + 28 ^2 = 33 ^2
    8 ^2 + 8 ^2 + 14 ^2 = 18 ^2
    8 ^2 + 9 ^2 + 12 ^2 = 17 ^2
    8 ^2 + 11 ^2 + 16 ^2 = 21 ^2
    8 ^2 + 12 ^2 + 24 ^2 = 28 ^2
    8 ^2 + 16 ^2 + 16 ^2 = 24 ^2
    8 ^2 + 20 ^2 + 25 ^2 = 33 ^2
    8 ^2 + 24 ^2 + 27 ^2 = 37 ^2
    9 ^2 + 12 ^2 + 20 ^2 = 25 ^2
    9 ^2 + 18 ^2 + 18 ^2 = 27 ^2
    10 ^2 + 10 ^2 + 23 ^2 = 27 ^2
    10 ^2 + 20 ^2 + 20 ^2 = 30 ^2
    11 ^2 + 12 ^2 + 24 ^2 = 29 ^2
    11 ^2 + 22 ^2 + 22 ^2 = 33 ^2
    12 ^2 + 12 ^2 + 14 ^2 = 22 ^2
    12 ^2 + 12 ^2 + 21 ^2 = 27 ^2
    12 ^2 + 15 ^2 + 16 ^2 = 25 ^2
    12 ^2 + 16 ^2 + 21 ^2 = 29 ^2
    12 ^2 + 21 ^2 + 28 ^2 = 37 ^2
    12 ^2 + 24 ^2 + 24 ^2 = 36 ^2
    13 ^2 + 26 ^2 + 26 ^2 = 39 ^2
    14 ^2 + 18 ^2 + 21 ^2 = 31 ^2
    14 ^2 + 22 ^2 + 29 ^2 = 39 ^2
    14 ^2 + 28 ^2 + 28 ^2 = 42 ^2
    15 ^2 + 18 ^2 + 26 ^2 = 35 ^2
    16 ^2 + 16 ^2 + 28 ^2 = 36 ^2
    16 ^2 + 18 ^2 + 24 ^2 = 34 ^2
    17 ^2 + 20 ^2 + 20 ^2 = 33 ^2
    18 ^2 + 18 ^2 + 21 ^2 = 33 ^2
    19 ^2 + 22 ^2 + 26 ^2 = 39 ^2
    20 ^2 + 28 ^2 + 29 ^2 = 45 ^2
    23 ^2 + 24 ^2 + 24 ^2 = 41 ^2
    24 ^2 + 24 ^2 + 28 ^2 = 44 ^2
    lol
    even Kronecker would like that

  • @evrik78
    @evrik78 Рік тому

    Outstanding: clear and easy to understand.

  • @asamonson6866
    @asamonson6866 7 років тому +4

    Again, you are awesome. You do a great job not just explaining the process but the reason behind it.

  • @noelabitzen6580
    @noelabitzen6580 2 роки тому

    UR MY LIFE SAVER

  • @MiKe-y8e
    @MiKe-y8e 4 місяці тому

    Thanks for your help may God bless you 🤝

  • @debendragurung3033
    @debendragurung3033 6 років тому +2

    ok , but what if we end up with polynomial expression under integral.
    eg
    X(t)= 2t
    Y(t) = 1+3t^2
    Z(t) = 2+ 4t^3

  • @ethanheikens5705
    @ethanheikens5705 8 років тому +9

    Thank you! Wish my professor taught this as well as you

  • @vincentwolfgramm-russell7263
    @vincentwolfgramm-russell7263 9 років тому +2

    Haha funny I was having trouble with this question. This question is from Stewarts Calculus: Early Transcendental!

  • @Zydico
    @Zydico 3 роки тому

    Thank you very much for this clear explanation. Explained much better than my textbook and professor's lecture combined with one example.

  • @jaredwright3342
    @jaredwright3342 Рік тому

    I thought you couldn't integrate a function with its parameter as a bound? i.e. how can t be the upper bound and be part of the function at the same time?

  • @maria1100
    @maria1100 2 роки тому

    omg youre the BESTTTTTTTT TYSM

  • @EricIskandarZulkarnain
    @EricIskandarZulkarnain 9 років тому

    thank it help alot i have final in 2 days time. but one quick question what if the end part of the question is change to with respect to arc length measured
    from (1,-1,2) in the direction of increasing t ?
    thank you !

  • @mimimoon1827
    @mimimoon1827 2 роки тому

    wow thank you so much!

  • @parad0x928
    @parad0x928 8 років тому

    Thank you very much, Your explanation was so clear and easy to follow (plus the question you solved happens to be the same i was looking at in my textbook).

  • @rolandsgradovskis9793
    @rolandsgradovskis9793 10 років тому +2

    wow thnx. i liked this so much i watched it 3 times in a row ha

  • @vinaydeshmukh8446
    @vinaydeshmukh8446 4 роки тому

    When you take the integral, doesn't there need to be a + C(vector) that you must calculate for using rvetor=0?

    • @cassied9327
      @cassied9327 3 роки тому

      This is a definite integral so we there will not be a +C
      :)

  • @wtfchazpwnt
    @wtfchazpwnt 6 років тому

    Very helpful video

  • @sleverlight
    @sleverlight 4 роки тому

    Wow thanks. I didnt know it was this easy the book was confusing

  • @theodorearmah3370
    @theodorearmah3370 4 роки тому

    Determine where on the curve given by r ⃗(t)=〈t^2,2t^3,1-t^3 〉 we are after travelling a distance of 20 units. Can someone help with the above question?

  • @heyitsrin6556
    @heyitsrin6556 4 роки тому

    Thank you!

  • @navyaaaa01
    @navyaaaa01 5 років тому

    What if the limits are not specified???

  • @tristan3577
    @tristan3577 4 роки тому

    What of my integral is a constant?

    • @kristakingmath
      @kristakingmath  4 роки тому

      Remember that the integral (with respect to x) of 3 is 3x, the integral of -7 is -7x, and the integral of k is kx. So integrating a constant just means you need to attach the variable to that constant.

  • @dwang2805
    @dwang2805 3 роки тому

    I encountered the exact problem and didn't know how to solve, came here, and found out that it is the exact problem, and even numbers match perfectly....

  • @romegulay2493
    @romegulay2493 9 років тому +3

    Thanks! it really helps a lot for my finals tomorrow. GOD BLESS :D

    • @kristakingmath
      @kristakingmath  9 років тому +2

      +Rome Gulay I'm glad I could help. Good luck tomorrow!

  • @Sameergupta1508_
    @Sameergupta1508_ 6 років тому

    omg....your voice is so sweet !!

  • @junebug9892
    @junebug9892 9 років тому

    Thank you for your help! The explanation was very helpful : )

    • @kristakingmath
      @kristakingmath  9 років тому

      +June Bug You're so welcome! I'm glad I could help!

  • @eswyatt
    @eswyatt 2 роки тому

    Some people substitute a dummy variable like "u" when they take the integral. I suspect it's less confusing to evaluate u by plugging in t than plugging in t or t. But the u really threw me the first time I saw it.

  • @kibrika
    @kibrika 6 років тому

    I'm confused as to why YT search for Krista's channel of "Chebyshev" gave out this video. I was hoping to get a nice example of how to use Chebyshev substitution. Not that this is not interesting, just unrelated.

  • @wasimakram-zf2xb
    @wasimakram-zf2xb 6 років тому +2

    Thank u ......may Allah's bless u

  • @BrooksHu
    @BrooksHu 2 роки тому

    tysm :)

  • @stephaniebeagle2030
    @stephaniebeagle2030 7 років тому +2

    This was very helpful! Thank you :)

  • @turkeydota2
    @turkeydota2 2 місяці тому

    Goat

  • @alemyatimothy3498
    @alemyatimothy3498 Рік тому

  • @MinhTri-io9om
    @MinhTri-io9om 8 місяців тому

    Jesus blesses for u

  • @trevor3905
    @trevor3905 3 роки тому

    thank you!