Area between a curve and the x-axis | AP Calculus AB | Khan Academy

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  • Опубліковано 4 лис 2024

КОМЕНТАРІ • 59

  • @Triyoger
    @Triyoger 9 місяців тому +3

    Almost 11 years and you’re still helping students out 💯

  • @sprmario524
    @sprmario524 6 років тому +38

    why is this 5 minute video more informative than my two hour calc class?

  • @Seafaringslinky
    @Seafaringslinky 11 років тому +16

    I've just got to say that you all are the biggest help in the whole world, thanks so much!

  • @ozzlicious
    @ozzlicious 10 років тому +79

    Everyone watch at 1.25x the speed. It is much faster and equally understandable. Good luck and God bless :D

    • @jason.stevens
      @jason.stevens 3 роки тому +2

      me watching at 2x speed

    • @ozzlicious
      @ozzlicious 3 роки тому +3

      @@jason.stevens Past me doesn't know what he's talking about. 2x is the only way to watch anything. 😉

    • @jason.stevens
      @jason.stevens 3 роки тому +2

      @@ozzlicious you know it man 😂 100%

  • @Dhanyerese1418
    @Dhanyerese1418 7 років тому +5

    Within 5 minutes, it became so clear! Thanks!

  • @spankymebottom
    @spankymebottom 6 років тому +3

    ty. the integral videos are superb and I'm having an easier time with this than limits themselves. is this usually the case for most people?

  • @vishalbhatia70
    @vishalbhatia70 7 років тому +2

    The sign for Integration comes from the LATIN LONG 'S' which essentially is short for Summa which in turn is short for SUMMATION which is what Integral Calculus is all about.
    Leibnitz was the first person to use that symbol!!
    The letters dx stand for INFINITESIMALLY SMALL particles of the variable x in this case
    Hope this helps.

  • @ilikebacon247
    @ilikebacon247 11 років тому +6

    that just alleviated my fear of definite integrals. I thought I had to evaluate it and get the sum of all values between the two numbers.

  • @bayekofsiwa5847
    @bayekofsiwa5847 8 років тому +3

    Made me learn it for about minutes..... OMG Commended Khan Academy!

    • @vtron9832
      @vtron9832 7 років тому

      Yeah me too, I never thought it would be possible to learn calculus and algebra in my class at the same time

  • @rando6662
    @rando6662 8 років тому

    Sal you are a lifesaver yet again!

  • @HenggaoCai
    @HenggaoCai 11 років тому

    You should post more practice problems online. Post some Optimization and related rates problems that are three times harder than the AP exam.

  • @fergiefergie4251
    @fergiefergie4251 8 років тому +39

    Slowing it down to .5 makes him sound drunk. lmao

  • @Kino-Imsureq
    @Kino-Imsureq 7 років тому

    its cool that when you have f1(x)=ax/|x| and you have variable A for an equation, the y axes will be flipped where y : 1 => y : -1 and y : -1 => y : 1 *IF* the point is below x : 0

  • @FrankEgan
    @FrankEgan 11 років тому

    Can you do a video on proving the area of a circle using integrals?

  • @richardmaurice5837
    @richardmaurice5837 7 років тому +30

    Here to study for a calc final tomorrow, anyone else?

  • @9898989878
    @9898989878 11 років тому +2

    Is there anything that I can do to help speed up the development of those integration practice exercises?

  • @Kino-Imsureq
    @Kino-Imsureq 7 років тому

    tried the equation on desmos it worked :)

  • @dan-lacks-commonsense6287
    @dan-lacks-commonsense6287 2 роки тому

    thank you very much

  • @TheALevelStudent1
    @TheALevelStudent1 11 років тому +1

    When do you plug in functions then? Isn't that definite integration?

  • @salsenani
    @salsenani 11 років тому +1

    Khan: 0:1 *&^%^&*&^^%^&*(*&^% 5:37
    me: ammmm !!!????
    khan : 5:38 sixty three over three, and three goes into sixty three exactly 21
    me : finally some thing i know

  • @vtron9832
    @vtron9832 7 років тому

    My video about definite Integrals is exactly like this but with real paper

  • @recursor9469
    @recursor9469 7 років тому +2

    Wait what about the plus c's? Is it acceptable to discard them and not even write them out in this situation?

    • @user-iq6zi3or3d
      @user-iq6zi3or3d 6 років тому

      recursor94 my same question

    • @peuchi1602
      @peuchi1602 6 років тому +2

      I had the same question, but I think it's because the constant would cancel out. It would be the same for both sides of F(b) - F(a), so doesn't matter what it is, it would be gone!

  • @kervincapangpangan4516
    @kervincapangpangan4516 6 років тому

    just a question though, where did you get f(x) = x^2 ?

  • @CryptowithKhalid
    @CryptowithKhalid 6 років тому

    this lecture contain super logy and concept

  • @TheGta4you
    @TheGta4you 11 років тому

    Sal I love u

  • @Parodox306
    @Parodox306 6 років тому +1

    You lost me at 3:43, where did that power rule come from?

    • @MadaoIsTaken
      @MadaoIsTaken 6 років тому +1

      Parodox306 it's the integral power role which is x^n+1/n+1

  • @vtron9832
    @vtron9832 7 років тому

    3:45 but is it not 2x instead of 3x^2? Also at the end he mentioned square units but exactly what square units?

    • @theshiningfalcon
      @theshiningfalcon 7 років тому +1

      At 3:45 I believe he took the derivative of x^3. Also the units can be anything, in the place of something like feet or meters you can just say units as none are specified.

    • @matthewvillarreal8297
      @matthewvillarreal8297 7 років тому +1

      Alef Nol look at the power rule when x^a. it ends up being (x^(a+1))/(a+1). end up as x^3/3+C

  • @143caoa
    @143caoa 10 років тому +2

    I freaking love you

  • @kevincooper2954
    @kevincooper2954 7 років тому

    why dont we put c constant of integration

    • @peuchi1602
      @peuchi1602 6 років тому

      I had the same question, but I think it's because the constant would cancel out. It would be the same for both sides of F(b) - F(a), so doesn't matter what it is, it would be gone!

  • @princessseraphina8990
    @princessseraphina8990 2 роки тому

    how did he get 64 again? My calculator does not have that

  • @sharmilaanne7997
    @sharmilaanne7997 5 років тому

    dx means what?

  • @bushraf9753
    @bushraf9753 4 роки тому

    I love you 💕❤️

  • @gabriellegall8278
    @gabriellegall8278 7 років тому

    I love you

  • @dcharles9158
    @dcharles9158 9 років тому

    I'm sorry, but am I the only one hearing a mosquito buzzing in the background (I have headphones on) I couldn't concentrate!!

    • @christinemartino5515
      @christinemartino5515 9 років тому +3

      Maybe it' s due to head phones ,just try to hear without headphones!

  • @reeceb4622
    @reeceb4622 6 років тому

    Someone say SIGMA?

  • @Auoric
    @Auoric 6 років тому +4

    Im wearing earbuds right now and it's so uncomfortable how I can hear every splosh of your saliva and every sniff of your nose. It is so distracting.