5.5 - The Substitution Rule

แชร์
ฝัง
  • เผยแพร่เมื่อ 1 ม.ค. 2025

ความคิดเห็น • 31

  • @jaredburgon8155
    @jaredburgon8155 5 ปีที่แล้ว +9

    It's unfortunate that I didn't discover you until the last unit of my Calc class, but I think you've single-handedly saved me and my Final Exam grade!
    p.s. Your handwriting is too good

    • @StaceyRoshan
      @StaceyRoshan  5 ปีที่แล้ว +1

      Jared Burgon this makes me so happy!!! So glad that these videos helped you prep for your exam. Sending so much luck your way if you haven’t taken it yet!!

  • @samwithsmalleyes5805
    @samwithsmalleyes5805 4 หลายเดือนก่อน

    Thank you so much for making this video.
    I know I am 8 years late to this, but I just want you to know 8 years ago you have saved countless student's grades through this video

    • @StaceyRoshan
      @StaceyRoshan  4 หลายเดือนก่อน +1

      You’re so kind to leave this message! Math should make sense, and I hope to make it feel that way for at least some others.

  • @tjs8433
    @tjs8433 28 วันที่ผ่านมา

    I've been working my way through chapter 5 since 1am for my unit test (4:45 now) thanks so much!

    • @StaceyRoshan
      @StaceyRoshan  27 วันที่ผ่านมา

      Wishing you luck on your test!!

  • @yuhsinchiu1444
    @yuhsinchiu1444 3 ปีที่แล้ว

    THANK YOU! I wouldn't have survived Calc AB without you, especially during COVID. These lectures are so good! Too good!

    • @StaceyRoshan
      @StaceyRoshan  3 ปีที่แล้ว +1

      I’m SO happy to be able to support your leaning this year. Thank you so much for the kind note. Hope you continue to have a lot of success in your course!

  • @jorgegonzalez-ec5fl
    @jorgegonzalez-ec5fl 6 ปีที่แล้ว +1

    Thank you!!! You are saving me so much time. I really appreciate your hard work in making these videos. It is very easy to follow and understand.

    • @StaceyRoshan
      @StaceyRoshan  6 ปีที่แล้ว

      I'm so happy to hear that!! Good luck in all your studying.

  • @bellezawei
    @bellezawei 7 ปีที่แล้ว +6

    Thanks for your lectures. It's very easy to understand ;))))

    • @StaceyRoshan
      @StaceyRoshan  7 ปีที่แล้ว +1

      I'm so happy that you've found my videos & that they're helping you out! Thanks for your kind note :)

  • @francesskulj6194
    @francesskulj6194 5 ปีที่แล้ว +1

    My university is currently on strike and I needed to learn integrals by myself before it was over! Thank you for your great lessons and helping me understand!

    • @StaceyRoshan
      @StaceyRoshan  5 ปีที่แล้ว

      I’m so so happy to hear this helped!! I hope your classes resume again soon. Good luck in your class!

  • @zakariazaki7513
    @zakariazaki7513 2 ปีที่แล้ว

    Thanks for video keep going 🤠 greeting from Morocco

    • @StaceyRoshan
      @StaceyRoshan  2 ปีที่แล้ว

      👋So glad you have found my videos! Wishing you good luck in your course :)

  • @akhaleed3448
    @akhaleed3448 5 ปีที่แล้ว +1

    Thank you for your amazing videos, it's really helpful. The way you are happy at the last example because the answer is 0 thou 😄

  • @boohoo4877
    @boohoo4877 6 ปีที่แล้ว +2

    thank you so much

  • @cordell5944
    @cordell5944 5 ปีที่แล้ว +1

    i don't know how u got 2/3 in the first example

    • @StaceyRoshan
      @StaceyRoshan  5 ปีที่แล้ว

      To take the antiderivative of x^n dx, we do 1/(n+1) * x^(n+1)... To oversimplify that, we add one to the exponent and divide by what we added. So, antideriv x^3 dx = 1/4 * x^4 + C. In our case, antideriv u^(1/2) du --> add one to the exponent: 1/2 + 1 = 3/2... and then dividing by 3/2 is the same as multiplying by 2/3... Therefore, we have antider u^(1/2) du = 2/3 u^(3/2) + C. Hope that helps!

  • @jasonaxe2082
    @jasonaxe2082 3 ปีที่แล้ว

    Where did the -8 come from for example 4?

    • @StaceyRoshan
      @StaceyRoshan  3 ปีที่แล้ว

      Do you mean how did I get du = -8x dx?

    • @jasonaxe2082
      @jasonaxe2082 3 ปีที่แล้ว

      @@StaceyRoshan yes

    • @StaceyRoshan
      @StaceyRoshan  3 ปีที่แล้ว

      @@jasonaxe2082 1. we identify u = 1 - 4x^2;
      2. we need to find du. just think of taking the derivative of each side of that equation -> du = -8x dx
      Does that help?

  • @evaristogabriel8208
    @evaristogabriel8208 5 ปีที่แล้ว

    i love youuuu

    • @StaceyRoshan
      @StaceyRoshan  5 ปีที่แล้ว

      So glad you're finding these videos helpful!!! Hope they continue to help :)

  • @drummerdog546
    @drummerdog546 3 ปีที่แล้ว +1

    peeb