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Homework Help: Help with an integration by parts problem

  1. May 24, 2007 #1
    integration problem :(

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

    int from 1 to 1/4 of [cos(pi*sqrt(t))] / sqrt(t) dt

    2. Relevant equations

    3. The attempt at a solution
    I tried using integration by parts

    used u = cos pi (sqrt(t)) and dv = sqrt(t), but got a really messy number as int of vdu

    so I tried u = sqrt t, du = 1/2sqrt(t)
    dv = cos pi*sqrt(t) , v = sin pi sqrt(t) * pi/2sqrt(t)

    So This doesn't seem right, how would I approach this problem?
  2. jcsd
  3. May 25, 2007 #2
    You want [tex] \int_{1}^{\frac{1}{4}} \frac{\cos \pi \sqrt{t}}{\sqrt{t}} \; dt [/tex]
  4. May 25, 2007 #3
    Yeah, but integration by parts didn't work, and I don't see how I can use substitution, any help?
  5. May 25, 2007 #4
    The change of variable method is correct.
    Put [itex]u = \sqrt t[/itex]
    [itex]2du = \frac{dt}{\sqrt t}[/itex]
    Substituting this will simplify the integrand. However, I think the mistake you are making is; you are forgetting to change the limits(1 & 1/4) of the integral. Whenever you make a variable change, the limits change according to the new variable.

    Hope this helps...
  6. May 25, 2007 #5
    multiply numerator and denominator by [tex] \sqrt{t} [/tex]

    You get: [tex] \int_{1}^{\frac{1}{4}} \frac{\cos \pi t}{t} \; dt [/tex]
  7. May 25, 2007 #6
    A substitution should work, try u=pi(t)^.5
  8. May 25, 2007 #7
    Hey, that's wrong :surprised. Multiplying [itex]\sqrt t[/itex] in the numerator doesn't change [itex]\cos \pi \sqrt t[/itex] to [itex]\cos \pi t[/itex].
    Last edited: May 25, 2007
  9. May 25, 2007 #8
    Oh wow... haha, yeah.. thanks.

    I was using u = cos pi(t)^.5

    Bah, thanks.
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