Trig substitution integration: x=a*sinθ, calculus 2

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  • Опубликовано: 30 июл 2024
  • In this calculus 2 tutorial, we will go over 4 examples on how to use the sine substitution to solve integrals. Use the time stamps below to help you navigate the video.
    0:00 When do we use x=a*sinθ
    0:49 Integral of 1/sqrt(a^2-x^2)
    4:12 Integral of sqrt(2-x^2)/x^2
    10:25 Integral of sqrt(1-4x^2)
    18:41 Integral of 1/(x*sqrt(9-x^2))
    ---------------------------------------------------------
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Комментарии • 41

  • @danieldanmola8266
    @danieldanmola8266 Месяц назад +1

    I don't know how well you know how to teach other aspect of math..but when it comes to math.. i give it to you🎉🎉😊😊

  • @Bbbbbx
    @Bbbbbx 2 месяца назад +3

    18:50 that moment of realization when u accidentally erased it was too funny

  • @aarnamishra5917
    @aarnamishra5917 Год назад +1

    thank you, this is really useful. Revising for my maths final and this is one area I've always struggled with, but after you explained it makes so much more sense!

  • @denisrudolph914
    @denisrudolph914 3 месяца назад +2

    Man the way you explain this stuff is insane thanks its really helpful !!!

  • @suryaprakash-lj8zz
    @suryaprakash-lj8zz 2 года назад +6

    just joined your new channel ......
    quality and free calculus for all....

  • @aaronwhite556
    @aaronwhite556 Год назад +16

    u almost forgot the "+ c!" you ARE human 😂

  • @stelios7702
    @stelios7702 2 года назад

    You are the best ever i saw in math world .i wish can met you one day

  • @user-cm6qm3he5v
    @user-cm6qm3he5v 9 месяцев назад +1

    wow your videos are very great nice well explained thank u sir🙂

  • @evangelinemcdonald9123
    @evangelinemcdonald9123 Год назад +1

    I love your videos

  • @newjsdavid1
    @newjsdavid1 Год назад +1

    doing three problems like this is helpful for me having attention span issues

  • @rogerkearns8094
    @rogerkearns8094 2 года назад +3

    These are good, thanks.

  • @Salamanca-joro
    @Salamanca-joro 4 месяца назад +2

    8:10 damn i was lost there i was like how can csc^2 become cot but i forgot this was integration not derivative

  • @MikeMitz-ef6rp
    @MikeMitz-ef6rp 3 месяца назад +2

    It's so helpfull

  • @aaronwhite556
    @aaronwhite556 Год назад +2

    I'm a burnt out cal 2 student and it is wholly disturbing how you simplify this!

  • @leena9708
    @leena9708 9 месяцев назад

    in problem 3 shouldnt you have multiplied the x= asinx by 2 to get what 2x is equal to? thank you'

  • @silentmath3198
    @silentmath3198 2 года назад +2

    Great Video!!!

  • @hydropage2855
    @hydropage2855 2 года назад +7

    That intro is so funny

  • @jacobschaumann
    @jacobschaumann 2 года назад +3

    Just wondering, where did you get your "ultimate calc 2 integrals" poster?

    • @bprpcalculusbasics
      @bprpcalculusbasics  2 года назад +3

      It’s my merch. You can check it out in the description 😃

    • @felipequinones5769
      @felipequinones5769 2 года назад +1

      I can’t buy your merch because it says me that my email address is not valid.😕
      Keep your good work!

  • @vitorsg
    @vitorsg 2 года назад +1

    Wow, super nice

  • @akashbhatti5141
    @akashbhatti5141 2 года назад

    Thank you sir

  • @wristdisabledwriter2893
    @wristdisabledwriter2893 2 года назад +5

    Quick question. If I was in your class and used x = acos(theta) and no errors would you be mad or give full points

  • @biniyab8416
    @biniyab8416 Год назад

    Pls can u help me this question?
    The integration of 2x cube minus 4x minus 8 over (x square minus x)(x square plus 4) dx or
    2x³-4x-8/(x²-x)(x²+4)dx

    • @matheusdossantos9252
      @matheusdossantos9252 6 месяцев назад +1

      I'm late but
      2x^3-4x-8 = 2(x^3-2x-4)
      x^2-x = x(x-1)
      Take the 2 out
      2 × integral of (x^3-2x-4)/x(x-1)(x^2+4)
      2 Is is a root of x^3-2x-4, when dividing x^3-2x-4 by x-2 we have the factorization
      (x-2)(x^2+2x+2)
      So, 2 × integral of (x-2)(x^2+2x+2)/x(x-1)(x^2+4)
      Well, I tried to simplify to eliminate some term but I didn't see a way, so lets to partial fractions
      (x-2)(x^2+2x+2)/x(x-1)(x^2+4) = A/x + B/(x-1) + (Cx+D)/(x^2+4)
      Well, this is the way

  • @hichamellouzati-fc6wj
    @hichamellouzati-fc6wj Год назад

    Good

  • @kianmath71
    @kianmath71 2 года назад

    Nice job

  • @rithvikthota
    @rithvikthota 2 года назад

    Good one

  • @GlobaliveKh
    @GlobaliveKh 7 месяцев назад

    🤩🤩🤩😍😍😍

  • @cosmicvoidtree
    @cosmicvoidtree 2 года назад +1

    Did anyone else notice the ambulance at around 17 minutes?

  • @georgesadler7830
    @georgesadler7830 4 месяца назад +1

    Thank you for the video. A plus C is needed after the integration is performed. For example, when you integrate d theta, you have theta, this is incorrect. The correct solution is theta plus a Constant. Please correct these errors in the video.

  • @TARRSS
    @TARRSS 3 месяца назад

    0:00 i⁴

  • @numberandfacts6174
    @numberandfacts6174 2 года назад +2

    Can u solve this if solve you are real mathmatician integration 0 to ∞ [ u^(s-1) ]/[ e^(u) + y ] ^(2) du 🥺

  • @Larry640
    @Larry640 Год назад

    my calc 2 professor took the whole hour and 40 minutes to explain this lmao

  • @mathevengers1131
    @mathevengers1131 2 года назад +1

    How do you upload videos on your so many channels regularly? I know you are a math wizard because you use teleportation spell at start of your videos.

    • @numberandfacts6174
      @numberandfacts6174 2 года назад +1

      Can u solve this if solve you are real mathmatician integration 0 to ∞ [ u^(s-1) ]/[ e^(u) + y ] ^(2) du 🥺

    • @numberandfacts6174
      @numberandfacts6174 2 года назад +1

      If u solve my problem then I coolbe with u I am also mathmatician I have a theroy to solve Riemann hypothesis 😑

  • @duetothefacthat
    @duetothefacthat Год назад +1

    fhuuuuaaaaaghk

  • @AWKUM469
    @AWKUM469 2 года назад

    Respected sir what's your religion pls reply me. I am mostly watching your video which is very helpful for us may Allah long live you.❤❤❤