Arc Length Calculus Problems,

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  • Опубликовано: 2 ноя 2024

Комментарии • 353

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Год назад +10

    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Next Video: ruclips.net/video/lQM-0Nqs9Pg/видео.html

  • @bhargavpatel6776
    @bhargavpatel6776 2 года назад +426

    I have noticed this common thing in all his videos that makes it really easy to understand each problem is that he does not skip any step, skipping small basic step can confuse students, leading them to fail tests. and for saving people like me thank you so much from the bottom of my heart.

    • @sonny1524
      @sonny1524 2 года назад +7

      Agree

    • @roblox21242
      @roblox21242 Год назад

      i have a c0cky teacher who skips lots of steps and then when i ask questions he says, you're supposed to kjnow because its from algebra/cal 1 etc....

  • @VenularSilver
    @VenularSilver 5 лет назад +380

    01:19 f(x) = 1 + 6x^(3/2); [0, 1]
    06:42 y = (3/2)x^(2/3); [1, 8]
    14:14 x = (1/3)(y^2+2)^(3/2); [0, 4]
    20:05 x = (1/3)(sqr(y))(y - 3); [1, 9]

    • @lilweez2175
      @lilweez2175 4 года назад +7

      Thanks bro. This vid is hard to follow if you skip around without time stamps lol

    • @eren8835
      @eren8835 4 года назад +4

      VenularSilver you got your prayer from me today my man

    • @carmenouzon6690
      @carmenouzon6690 7 месяцев назад

      What’s crazy is 4 questions took him 30 minutes to explain

    • @selinm
      @selinm 6 месяцев назад +1

      @@carmenouzon6690 Because he explains each step in detail so that you can watch and learn when you get stuck. This is what distinguishes him from the lecturers at the university.

  • @sureshmahadho1355
    @sureshmahadho1355 4 года назад +106

    To the organic tutor, I just wanted to say thank you so so much for all your videos, I am currently in my final year teaching, and am majoring in mathematics and science. I would not have been able to do it without your videos. Your methods are amazing and its simple to follow your explanations. God bless.

  • @DEATH25151
    @DEATH25151 Год назад +24

    We need more people like you. Who explains. Everything. Like every step and detail. Like really in DETAIL. Even though we know some stuff. It's better for someone like you to explain in full detail. So that it is really understood. ❤

  • @fluffyzozo1629
    @fluffyzozo1629 3 года назад +533

    how is getting a volume easier than getting length in calculus, HOWWWW!!!!!

    • @J0HnNyX
      @J0HnNyX 3 года назад +18

      Because in order to get volume you need the dimensions first.

    • @hadassah5063
      @hadassah5063 2 года назад +4

      🤣🤣

    • @chickenleg8824
      @chickenleg8824 2 года назад +8

      And there’s no proof for arc length of the curve however for volume formula there’s at least intuitive explanation

    • @474yx
      @474yx 2 года назад +5

      Someone PLEASE HELP! this is a bad question, but for the first example, he didn’t substitute u back in for what it was (1+81x) why?!?!!!!!!

    • @hahahamamamama2535
      @hahahamamamama2535 2 года назад +5

      @@474yx it was a definite integral

  • @dekartkosa1598
    @dekartkosa1598 7 лет назад +270

    I love you so much man, you are saving me right now in calculus 2!!

    • @AsaWRLD47
      @AsaWRLD47 4 года назад

      @Ian Taylor How much homework do you get in college calculus?

    • @AsaWRLD47
      @AsaWRLD47 4 года назад

      @Ian Taylor Were the problems like part a b c defglwgwnaoeu?

    • @videobyandrew
      @videobyandrew 3 года назад +6

      @Ian Taylor Literally me right now. I'm at exactly a 60% in my calc class and tomorrow is the final, this is determining if I pass or fail

    • @videobyandrew
      @videobyandrew 3 года назад +2

      @Ian Taylor Haha thanks, you too!

    • @tylerlarson532
      @tylerlarson532 2 года назад +2

      @@videobyandrew homie did you pass or nah

  • @freakyneurolink
    @freakyneurolink 4 года назад +184

    college has been so difficult to keep up with these past few weeks that i’m reviewing all this stuff the day before the test :(

    • @songohan3042
      @songohan3042 3 года назад +11

      you are not the only one
      lmao

    • @faizuuasif367
      @faizuuasif367 3 года назад +4

      i feel you

    • @aniketmukhia8355
      @aniketmukhia8355 3 года назад +10

      Lmao im in the one night before exams gang

    • @Elicruz2
      @Elicruz2 3 года назад +10

      @@aniketmukhia8355 got one tomorrow, can't wait to fail!

    • @colbylewis8543
      @colbylewis8543 3 года назад +4

      @@Elicruz2 U will not fail

  • @XxFBoxX
    @XxFBoxX Месяц назад +1

    This is the first time a teacher of mine has explained a concept clearer than you. A testament to my calc II teacher a few years back, and even more so to you for being better than the hundreds of teachers I’ve had.

  • @AsaWRLD47
    @AsaWRLD47 4 года назад +19

    Self-studying for Calc BC. Oof, talk about procrastination. One of the few good things that came out of the pandemic is the shortening of the AP tests. I should probably still learn the rest of the stuff so I'm not confused later on lol.

  • @georgesadler7830
    @georgesadler7830 2 года назад +7

    Professor Organic Chemistry Tutor, thank you for another beautiful video/lecture on Arc Length Problems in Calculus Two. Calculating Arc Lengths in Calculus is straight forward, however, the Algebra and the Integration can get messy. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.

  • @kingfedat2944
    @kingfedat2944 3 года назад +107

    Crazy how I can literally watch 6 min of this video and understand the topic but won’t even understand a word from my professor 120 mins lecture.

    • @ericbenaim4297
      @ericbenaim4297 3 года назад +2

      same bro same

    • @melenihasanovic5198
      @melenihasanovic5198 3 года назад

      literally

    • @ManoDGoat
      @ManoDGoat 3 года назад +11

      I think it's because you've already got over the hard parts of wrapping your mind around the new information. When you come to yt...you already have a sort of foundation.. which is probably why it feels easier here..
      That's just my theory cause it happens to me too

    • @GooseCrack
      @GooseCrack Год назад +2

      @@ManoDGoat I think that makes sense, sometimes a second step by step helps a lot

  • @natemac8473
    @natemac8473 5 лет назад +384

    Ok can I just say this: arc length integrals suck.

    • @figgiano
      @figgiano 5 лет назад +12

      this is easy

    • @emmanuelonyeagba8276
      @emmanuelonyeagba8276 4 года назад

      Nate Mac I love calc II

    • @TheTacticalMess
      @TheTacticalMess 4 года назад +56

      King Figg The actual integration is easy. Getting into a form where it’s easily integrable is straight up annoying.

    • @AdityaSUnboxings
      @AdityaSUnboxings 4 года назад +24

      @Naomi Nagata ur right, its easy, but actually integrating some of the stuff, and especially spending 15 + minutes trying to integrate and finding out you were integrating wrongly or that the integrand is nonelementary, is just sad.

    • @natemac8473
      @natemac8473 4 года назад +2

      I'm now in Diff Eq and doing Laplace transform and I want to rip my hair out.

  • @zoesteele6745
    @zoesteele6745 2 года назад +9

    You’re videos are a lifesaver! I felt somewhat comfortable with arc length before watching, but after watching I felt confident in my work!

  • @josh1234567892
    @josh1234567892 4 года назад +15

    At 18:11 I'd like to also add that it helped me to just use u-substitution to let u = y^2, so you can just factor u^2+2u+1. It's easier for me to remember because we use u as the variable for u-substituting integrals as well.

    • @474yx
      @474yx 2 года назад

      Someone PLEASE HELP! this is a bad question, but for the first example, he didn’t substitute u back in for what it was (1+81x) why?!?!!!!!!

    • @si1az0
      @si1az0 2 года назад +1

      @@474yx because he found the new integral by plugging the values of x into the equation that U equals and therefore found new bounds for the integral (:

    • @Zoooooooooooo
      @Zoooooooooooo Год назад

      @@si1az0 rocket league?

    • @si1az0
      @si1az0 Год назад +1

      @@Zoooooooooooo ?

  • @bm8524
    @bm8524 7 месяцев назад

    Thank you thank you thank you so much for writing out all the steps. My prof goes so fast and skips stuff when writing everything and it kills me cause I just can’t catch up that quickly. Even some yt vids skip some things and I just appreciate how in depth these vids are.

  • @m_ma28
    @m_ma28 5 лет назад +7

    I watched most of your calculus videos and they’re just the best thank you!!!

  • @nicomez3319
    @nicomez3319 5 лет назад +14

    This mans a true genius, thank u for saving my gpa on an array of occasions

  • @nicholascalderon1008
    @nicholascalderon1008 10 дней назад

    once again youve done it again. you are the best thing thats ever happened to math

  • @antoniodbz5850
    @antoniodbz5850 4 года назад +3

    I think this is the first time I find a hard example. Especially the last one.

  • @MdeM8
    @MdeM8 6 лет назад +11

    you are the best! you've saved my butt numerous times. thank you

  • @domdubz7037
    @domdubz7037 4 года назад +5

    The procedures to this our easy. I really wish you went more into detail about what’s happening and why we’re doing these things and explaining what the answer means and is telling us.

    • @caleblee2824
      @caleblee2824 2 года назад +1

      Its probably because he goes more indepth on his patreon usually.

  • @samquick5859
    @samquick5859 3 года назад +7

    They need to clone Organic Chemistry Tutor and have him teach all STEM-related classes from the high school to college levels

  • @marionettes7974
    @marionettes7974 5 лет назад +19

    holy shit, the last problem is actually the one that I am working on and stuck on...

    • @sadtrash4623
      @sadtrash4623 3 года назад

      I found one of my problems here, too

  • @johnpringle9967
    @johnpringle9967 4 года назад +10

    At the conclusion of example problem 2 around (14:00), you didn't convert the "u" substitution back to its original value (1+ x ^2/3) before making the final calculations. I'm wondering why? I'm new at this, so if it's a stupid question, you have my apologies. When I did convert it back, I got a decimal answer of 3.611. Thanks for your videos. I take extensive notes from them and follow your work closely.

    • @yearofsilence
      @yearofsilence 2 года назад

      I got the same thing... I think he forgot to substitute back.. :( He never answered you... sigh

    • @geckokun2805
      @geckokun2805 2 года назад +3

      ​@@yearofsilence when using u-substitution, you wont need to substitute it back if you replaced the a and b values with their u values before integrating. Notice he changed 8 and 1 to 5 and 2

    • @yearofsilence
      @yearofsilence 2 года назад +1

      @@geckokun2805 So if you don't change the values from 8 &1 to 5 and 2 then , in that case, you would have to substitute it back? it's been a while haha

    • @caleblee2824
      @caleblee2824 2 года назад

      @@yearofsilence With U sub if you find U(b) and U(a) you don't need to substitute U back in but rather directly insert U(b) and U(a) as U. I'm not sure if you can do it any other way

  • @coledicke
    @coledicke Месяц назад

    yo you are literally a genius. it's insane

  • @emfoovigi185
    @emfoovigi185 10 месяцев назад

    I found the factoring out in the 2nd problem kinda weird so I tried the approach I immediately thought of instead which was trigonometric substitution, and it actually worked as well!!

  • @smokingfox4165
    @smokingfox4165 7 месяцев назад +1

    Saving me in Cal 2, Thank you so much for your teaching.

  • @xevvs9440
    @xevvs9440 2 года назад +3

    you deserve my lazy teacher's salary. thank you for this.

  • @captaincrumble837
    @captaincrumble837 2 месяца назад

    Awesome content! The way you explain complex topics in such a simple intuitive way is just amazing! Thank you, for all the math help!

  • @johngalan3754
    @johngalan3754 6 лет назад +11

    You're a patron of the arts

  • @evrchng
    @evrchng 28 дней назад

    lol right aroung 25:04 I am pausing the video as I usually do, this time questioning my decisions on major, but trying to comprehend the method. Only to press play and the very next words "This is going to be a long problem" confirms that I am not overexagerating my grief.

  • @flow_987
    @flow_987 2 года назад

    Organic Chemistry Tutor, you are a legend.

  • @simplyydee
    @simplyydee 5 месяцев назад +2

    I’m a bit confused on why we change [a,b] when using u sub. but thank you for this video💯

    • @simplyydee
      @simplyydee 5 месяцев назад +1

      From what i understand, if you want to keep the problem in terms of “u” like he did at 5:27 of the video, you change the limits of integration as he did. So instead of replacing u with (1 + 81x), he changed the [a,b] values to make it easier. So if you want to keep the “u”, you gotta change the limits of integration. If you plan on replacing “u” back with whatever number was subbed out ( 1+81x in this video) then you do not need to change the limit of the integration. Hope that helps for anyone who may have been confused like myself. It makes perfect sense once you understand!

    • @I61void
      @I61void 4 месяца назад +1

      he basically just skipped to a upcoming step and did it there for easier understanding... you could do it later when you implement whatever u equals

    • @simplyydee
      @simplyydee 4 месяца назад

      @@I61void yes thank you, i’m well acquainted with these concepts now.

  • @Rushman666
    @Rushman666 Год назад +3

    I am finding the arithmetic absolutely brutal for these problems

  • @ptyptypty3
    @ptyptypty3 4 года назад

    wow, is this guy the best? or what? .. THANK YOU.. you're a genius......

  • @brhaneyemane7185
    @brhaneyemane7185 Год назад

    I deeply thank for your funny explanation and, I am awaken during the whole explanation, such brilient thanks!

  • @beentertainandlearn5560
    @beentertainandlearn5560 7 лет назад +6

    you really a very good teacher..

  • @nananabaka1128
    @nananabaka1128 5 лет назад +1

    thanks so much never been i watch a vid tutorial that is very informative n helpfull.. i loveu

  • @108Irvine
    @108Irvine 2 года назад

    You have a superb art of teaching

  • @dahliav.1583
    @dahliav.1583 Год назад

    thank you for your calculus videos ! they are the reason i understand integrals

  • @Nzargnalphabet
    @Nzargnalphabet 10 месяцев назад

    Thanks, using this to find the circumference of a squircle

  • @3110-l6n
    @3110-l6n 3 года назад +1

    Thank you so much for making your content free

  • @TheLEGOKID2000
    @TheLEGOKID2000 5 лет назад +7

    For the second question why weren't we able to do U substitution immediately and instead have to factor out the x^(-2/3)?

    • @EL-ISS
      @EL-ISS 4 года назад

      because if you don't the question becomes a lot more confusing to do, factoring out the X^(-2/3) makes it easier to solve without the use of computing power.

  • @pappples
    @pappples 4 года назад +7

    shouldn't the index number of 2/3 be 3 and not 2 for the second one? 1/2 is a square root and 1/3 is a cubed root so I'm just confused(@10:34 in the video)

  • @ryangroom2959
    @ryangroom2959 2 года назад +6

    On the second problem I’m a little confused, why wouldn’t you just leave the limits of integration the same and put the equation back in terms of x after the u sub? That’s what I did and I got a different approximate answer

  • @mohsenamini3297
    @mohsenamini3297 4 года назад

    JG God bless you, I learned a lot from your video clips. Your instructions are very clear, to the point........

  • @vinceojeda7215
    @vinceojeda7215 2 года назад

    Thank you so much to this channel.^^. Really appreciate your videos. More power an Godbless.💖💖

  • @ibrahimimran6197
    @ibrahimimran6197 2 года назад +4

    btw how would we know if we are to use u substitution right after finding f prime of x or first take x common outside the parentheses , create two separate square roots and then use u substitution?

  • @solascriptura911
    @solascriptura911 3 года назад

    this man is a serious genius, NASA-stuff

  • @adansilva6851
    @adansilva6851 4 года назад

    that last question was gnarly

  • @T3m0ur
    @T3m0ur 5 лет назад +2

    Great vid buddy! Helped a ton!

  • @SHENUM.
    @SHENUM. 3 года назад +3

    Soooo helpful.
    Keep it up man😉❤

  • @fastonmphande5314
    @fastonmphande5314 3 года назад

    nice presentation sir JB

  • @domanicmarcus2176
    @domanicmarcus2176 3 года назад +5

    Thank You sir for the video, but I think starting at time 17:29, it should have been dy and not dx at the end of the integral. Am I correct?

  • @fatimahosman7476
    @fatimahosman7476 3 года назад

    That ad of prof.David costa scared Me 😂😂😂😂😂until i came back to my sense

  • @faizuuasif367
    @faizuuasif367 3 года назад

    this man is an angel

  • @asadullah23200
    @asadullah23200 5 лет назад +35

    If God asks me who should go to heaven I say you. Even tho God will never ask me that

  • @brax300
    @brax300 Месяц назад

    Oh yeah boys. I’m so fucking COOKED for this exam. Great 👍🏽

  • @felixnkumbira3169
    @felixnkumbira3169 4 года назад

    this tutorial is the best

  • @isaaconyach9401
    @isaaconyach9401 6 лет назад +6

    i wish i could pay you for this. thank you

  • @MasterEngineerPh
    @MasterEngineerPh 2 года назад +1

    Correction at 13:35, it is supposed to be 2/3 because you took the derivative not the integral hence multiplying gets us 4/9. Agree?

  • @OHHS2
    @OHHS2 Год назад

    أحبببك يا أحلى أستاذ❤❤❤❤🔥🔥🔥🔥🔥

  • @davidm3210
    @davidm3210 5 лет назад +3

    He's fantastic but has a tendency to belabor simple algebraic/math operations and burn through the harder concepts -anyone else notice that? Check out Krista KIng's video (Arc Length ..) for the last problem, I think that she executes it more clearly.

  • @whenwhyhow2449
    @whenwhyhow2449 5 лет назад

    Nice channel for students 👍👌

  • @uduakubokudom6076
    @uduakubokudom6076 3 года назад

    You are doing well sir

  • @cresandrewremulta4667
    @cresandrewremulta4667 3 года назад

    Thanks for teaching us sir

  • @uoieavillanueva5806
    @uoieavillanueva5806 3 года назад

    You're legendary man

  • @frenshyruiz7267
    @frenshyruiz7267 6 лет назад

    your the math goat.

  • @vincenciussufijanhadi1287
    @vincenciussufijanhadi1287 Год назад

    Exercise .
    a. f ( x ) = 1 - x ^ 1/2, with x = 0 to x = 1.
    b. f ( x ) = 1 - x^ 1/3, with x = 0 to x = 1.

  • @jugalnaik68
    @jugalnaik68 6 лет назад +1

    Youu saved me in my first exam

  • @robertherd4579
    @robertherd4579 3 года назад

    Love your videos bro ❤️

  • @ViNncentSmith
    @ViNncentSmith 3 года назад +3

    2:23 WHATS 6 TIMES 3 ?
    6 TIMES 3
    6 THREES
    this a a refrence to a meme xD

  • @GwynsFate
    @GwynsFate 3 года назад +1

    When and why do we have to change the limits of integration? I'm guessing that it has to do with u-sub but I'm unsure.

  • @miguelposada3684
    @miguelposada3684 Год назад +1

    i have a question about the last problem when you factor the 1/4y^-1, shouldn't the new expression have the 4y+1(y-1)^2 to account for the term that has been factored? because I see that you factor it as (4y+(y-1)^2) I feel confused in this part

  • @hlulanidzavana6126
    @hlulanidzavana6126 6 лет назад

    maman I really thank you and I hope you can do double integration under solid revolution topic thangs man.

  • @UnforgivingMotors
    @UnforgivingMotors 3 месяца назад

    7 years later still helping students out o7

  • @andrewisaac9599
    @andrewisaac9599 4 года назад

    Thanks. This was really helpfull

  • @graceyboman1798
    @graceyboman1798 4 года назад +2

    On the last question does he cancel one of the 3's twice? he cancels the 3 from 1/3 at 21.18 and then again at 22.04...

  • @babai08_
    @babai08_ 3 года назад +1

    For the last one I integrated by parts and the final answer was the same. If you did it the same way as I did, it is correct as well.

  • @tasneemayham974
    @tasneemayham974 Год назад

    At 10:34 , may anyone please tell me why did he factor out x^-2/3? Why didn't he go directly for substitution?
    AND THANK YOU SIR FOR ALL THESE AMAZING VIDEOSS!!

    • @kamogelomolepo4285
      @kamogelomolepo4285 Год назад +1

      I’m also confused but I think it has something to do with the exponents being negative or something,I’m just assuming cause he did the same with the other problem

  • @Toppersvilla
    @Toppersvilla 6 лет назад

    You are great !
    From india

  • @m4rr563
    @m4rr563 4 года назад +6

    in the first problem why do you need to change the bounds? 3:55

    • @augustinkim7538
      @augustinkim7538 4 года назад +1

      I'm not sure if you figured out as to why he changed the bounds of the integrals. If not, it's because he used the u-sub which caused him to change the bounds. You can keep the same bounds if you remember to change the u value back in terms of x.

    • @m4rr563
      @m4rr563 4 года назад +2

      Augustin Kim yeah I figured it out like 4 months ago. Thanks anyways. I passed Calc 2 with an A

    • @augustinkim7538
      @augustinkim7538 4 года назад

      @@m4rr563 congratulations, I'm taking calc 2 now.

  • @m_ma28
    @m_ma28 5 лет назад

    You are the best

  • @EL-ISS
    @EL-ISS 4 года назад +1

    why don't you plug the u-sub back in? Like you immediatly put in the values without reverting U back to the x function that it stands for.

  • @kylakristie8338
    @kylakristie8338 6 лет назад +4

    Saved my dumb ass. Thank you!!

  • @huffaz_group
    @huffaz_group 6 лет назад

    Sir you are genius

  • @peterselemani9880
    @peterselemani9880 4 года назад +3

    sir, why do we find the new limit in our context above when its f(x) but not f(y)??

    • @asalah1672
      @asalah1672 4 года назад +2

      You only change the limit when using u-sub. If you are not going to replace u then you need to change the limit boundaries

    • @hsadikhova8602
      @hsadikhova8602 3 года назад

      @@asalah1672 thanks😅

  • @AnastasiaAlepio
    @AnastasiaAlepio Месяц назад

    Thank you. I've got one question, can anyone help. why are some limits changed using u-substitution and some don't?

  • @jiaxinli1674
    @jiaxinli1674 5 лет назад

    the voice is really like the Lenard in Bigbang Theory.

  • @pmccannedu
    @pmccannedu 6 лет назад +1

    Thank you !

  • @brotherdom7661
    @brotherdom7661 Год назад +1

    Can you leave the original [_,_]? For the first you changed [0,1] to [1,82] but I left it and still got the same answer

  • @Messengers966
    @Messengers966 7 лет назад

    I really appreciate you sir

  • @batuhanayhan
    @batuhanayhan 4 года назад

    there is an easy step you guys take in the last question.After derivating and taking square you add plus 1 and you can apply completing square method.

  • @jessedossey1442
    @jessedossey1442 4 месяца назад

    *6 minutes into the problem*
    OCT: this is gonna be a long problem

  • @TalhaKarakoyunlu
    @TalhaKarakoyunlu 2 года назад

    Thanks!

  • @mechboy5954
    @mechboy5954 6 лет назад

    Great video

  • @pistachio66
    @pistachio66 4 года назад

    Why do you do 1 divided (1y^-1)/4 instead of (1y^-1)/4 divided by 1 when factoring? You don't know which number is bigger. This is at 25:50 minutes in

  • @jazminee3601
    @jazminee3601 5 лет назад +49

    you are like freaking Jesus

  • @XzLibertyzX
    @XzLibertyzX 2 года назад

    I have a question? Why can’t you use usub for 9:00, wouldn’t it work out like the last problem did.
    U = 1 + x ^ -2/3
    Du= -3/2 x ^ -5/3

    • @XzLibertyzX
      @XzLibertyzX 2 года назад

      Nvm you can’t square root it after just thought about it