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Homework Help: Integration by Substitution

  1. Oct 1, 2007 #1
    1. The problem statement, all variables and given/known data

    problem.jpg


    2. Relevant equations

    None. Well, dx=du/cosx

    3. The attempt at a solution

    I've substituted it in, got new values for the limits but I have u^-1 on the bottom and so can't integrate it from my current knowledge. Basically I'm stuck with:

    Integration of u^(-1) du with limits of 1 and 2.

    Any help appreciated. Apologies for not being able to work the Latex system.
     
  2. jcsd
  3. Oct 1, 2007 #2

    arildno

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    Seriously, you haven't encountered the derivative of the natural logarithm yet?
     
  4. Oct 1, 2007 #3
    I have but I thought it had to be a linear expression to use the natural log. It did cross my mind though - this is what to do, then?
     
  5. Oct 1, 2007 #4

    arildno

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    What do you mean by a "linear expression"??
     
  6. Oct 1, 2007 #5
    Something of the form (ax+b).

    Decided to assume that (u) is in that form and so worked it through. Is ln(2) the final answer?
     
  7. Oct 1, 2007 #6

    arildno

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    Ask yourself:
    May we write u=1*u+0?

    Sure, the answer is ln2
     
  8. Oct 1, 2007 #7
    Thanks for your help! :)
     
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