Arc Length Examples | Calculus 2 - JK Math

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  • Опубликовано: 15 дек 2024

Комментарии • 6

  • @cynthiawu5342
    @cynthiawu5342 8 месяцев назад +4

    u the best!

  • @carriverwow
    @carriverwow Месяц назад

    could you please do a short video on integration by tables if you ever get the chance? Its the only topic in my calc 2 class so far that you haven't had a video for!

    • @JKMath
      @JKMath  Месяц назад +1

      Hi! I have no current plans to make a video on integration by tables (IBT), but the general process of IBT is to look at your integral you want to solve, and match it to one of the formulas in the "tables," of which there are nearly 100 to choose from. Typically there will be a "u" that you need to account for. For example, you could have the integral of (x-1)e^(x-1), and using the formula from the table it matches the integral of ue^u where u=(x-1). So using the formula that the integral of ue^u is (u-1)e^u+C, the integral would be (x-2)e^(x-1)+C.
      Really, IBT is just a shortcut method for integrating without doing all the work by hand - you can skip right to the answer by matching the integral to a form represented by a formula in the tables (usually the tables are in the appendix of your calculus textbook, although I'm sure you can find them online as well). I don't cover this topic in a video because there are so many formulas (as I said, about 100), and the majority of them are already based on integration methods/formulas we already know/learned earlier in calc 1 and calc 2. So in most cases it is probably quicker to do it by hand rather than spending time trying to find the right formula in the tables. Additionally, since you need the tables of formulas to do IBT, its very unlikely you would be tested on this method unless given the tables to use. I would hope no one expects you to memorize all those formulas! Hope this helps :)

    • @carriverwow
      @carriverwow Месяц назад

      @ thank you!

    • @carriverwow
      @carriverwow Месяц назад

      @ my teacher seems to put more emphasis on integration by tables than most. She gave me half credit for doing what you just described so I’m somewhat at a loss as to what she wants.

    • @JKMath
      @JKMath  Месяц назад +1

      ​@@carriverwow You may need to check in with your teacher to see exactly how she wants you to approach those problems then, or go back and reference your class notes. It's possible you chose the wrong formula from the table for your problem, but if you did pick the right one, you also want to make sure to state which formula you used (the number associated with the formula from the tables you use), and you want to write out what each part is equal to. So if you are using a formula that involves placeholders of u, a, b, du, etc, you want to be sure to explicitly write out what each of those are equal to in your original integral. When I look at examples of using integration by tables in my calculus textbook, that is all they do as well. Hope this helps!