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Integration by substitution

  1. Jan 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Evaluate the definate integral of the following
    [tex]\int[/tex] (from 1 to 2) [tex]\frac{sin t}{t}[/tex] dt

    3. The attempt at a solution

    I am actually stuch from the very beginning.
    I tried to set u=sin(t) but this doesn't help much because (sint)'=cost and
    this is going to make the problem more complicated.
    I also set u=1/t but the derivative of 1/t has nothing to do with
    the function as well.

    (Perhaps I shouldn't integrate the function by substitution)

    Please help me with the start!!
  2. jcsd
  3. Jan 23, 2008 #2
    I set:
    u=sint dv=1/t dt
    du=-cost v=lnltl

    [tex]\int[/tex] [from 1 to 2] (sint)(1/t) dt

    = [(sint)(lnltl)][tex]^{1}_{2}[/tex] -[tex]\int[/tex][from 1 to 2] lnltl (-cost)

    How do I integrate the red part?
    should I do the by parts again?
  4. Jan 23, 2008 #3


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    Homework Helper

    Well...I do not think there is any closed form of that integral.(To my knowledge) You may need something more than integration by parts.
  5. Jan 23, 2008 #4
    For your latex


    \frac 1 t or \frac{1}{t} - use the brackets when you have more than one letter per term

    Or maybe you were lazy :-p
  6. Jan 24, 2008 #5


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    Homework Helper

    roco, where did you learn the \int_1^2 notation? I never figured it out, at least not from the latex code reference PDF file.
  7. Jan 24, 2008 #6

    Click on the latex and you will see the code.
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