Integrating Exponential Functions with Substitution | Calculus 1 Exercises

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  • Опубліковано 10 гру 2024

КОМЕНТАРІ • 14

  • @Gojover
    @Gojover Рік тому +1

    I always get confused at functions that are ambigously show themselves as two different ones but are two of the same type. Like in q3 here. I thought this would need integration by parts for -2x^3= algebraic and e^-x^4 = exp. Thats what im looking for in ur videos like which one to take as multiple func and which one not

    • @WrathofMath
      @WrathofMath  Рік тому

      My advice would be to always check for u-sub before moving onto a more complicated solution like parts. With practice, you should be able to recognize when you have something like x^2sin(x^3), we see u-sub works because the function inside the sine has a derivative equal to a multiple of the other function. Or, x^(-2)e^(x^-1), same idea.
      For Q3 in the video, If you were to try parts and set v = e^-x^4 you'd quickly arrive at an impasse, since we cannot integrate that into elementary functions. If you set u = e^-x^4, you'd probably realize you should be using u sub once you found du/dx = -x^3e^-x^4.
      Always stay on the lookout for u-sub! Another kind that's easy to miss is something like sin(sqrt(x)) / sqrt(x).

  • @J_Lynn
    @J_Lynn Рік тому

    at 7:00, I have this exact problem on my homework and it's showing this answer as incorrect. Not really sure what else to do!

    • @WrathofMath
      @WrathofMath  Рік тому

      No idea - perhaps you're misreading the homework problem? The solution in the video is correct. If you're not misreading the problem, then the answer key must have a typo.

    • @prash56
      @prash56 Рік тому

      @@WrathofMath no, you are wrong.

    • @WrathofMath
      @WrathofMath  Рік тому +2

      No I’m not, but I’d be happy to tell you where you are wrong if you can tell me where you think I am wrong

  • @asfah301
    @asfah301 Рік тому

    What should I do when I get (-x dx) after substitution and in question I got x^3 dx

  • @Gojover
    @Gojover Рік тому +1

    Can you tell whats the sequence in which these functions should be done is it ilate or liate

    • @WrathofMath
      @WrathofMath  Рік тому

      I'm not sure what you mean, what is ilate and liate?

    • @Gojover
      @Gojover Рік тому

      @@WrathofMath its an abreviation of inverse. Log. Algeraic. Trig. Exp

  • @user-pt9zy5pb2d
    @user-pt9zy5pb2d 2 роки тому

    Sir, how do we solve this?
    Use a proof by contradiction to show that if 𝑛2 − 1 is odd, then 𝑛 is even.

  • @Gojover
    @Gojover Рік тому

    I always make the dx the whole subject of du with nothing on the dx side in this case tried to do -1/4x^3 du = dx and got the same answer

    • @WrathofMath
      @WrathofMath  Рік тому

      That works fine - but to me it always seems like a waste of time to do it that way. I don't know if I talk about why I do it the way I do in this video. If not, maybe I do in this one: ua-cam.com/video/qhnHDr1g4sY/v-deo.html
      Not a big deal either way though - whichever way makes more sense to you, they're both the same at the core!

  • @gabbyr1064
    @gabbyr1064 7 місяців тому

    why did you just make this more confusing