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Homework Help: Integral troubles

  1. Apr 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Alrighty. I have reduced a vibrations problem to an integral and I am having some trouble
    evaluating it.

    I have a value for t and need to find:

    [tex]-c\omega^2Z^2\int_0^t\cos^2(\omega t-\phi)\ dt[/tex] (1)

    I guess it is just my memory that is the problem.

    If I had [itex]\int\cos^2(x)\ dx[/itex] It would not be a problem.

    I am thinking now that I type this that a simple U substitution should do the trick right?


    If I let [itex]u=\omega t-\phi\ \Rightarrow du=\omega\ dt[/itex]

    So (1) becomes:

    [tex]-c\omega Z^2\int_0^t\cos^2u\ du[/tex]

  2. jcsd
  3. Apr 5, 2009 #2


    User Avatar
    Homework Helper

    hi - i think your limits should become u(0) & u(t) as well
  4. Apr 5, 2009 #3
    If you just use the the double angle formula
    [tex]\cos^2 t = \frac{1}{2} (1+\cos 2t) [/itex]
    from the outset (because it's the next step after your u-substitution anyway), then you really don't need to do a u-substitution if [itex]\omega[/itex] and [itex]\phi[/itex] are just constants.
  5. Apr 5, 2009 #4
    pls help me too...integration problem

    hi.... i am new here and i hope someone can please answer my question too..

    x-1 + dk/dy = x-1
    so when we cancel both x-1 we get dk/dy = 0

    my question is can i integrate dk/dy to get the k's value??

    if i integrate dk/dy, am i getting C (constant) for the k value???

    thank u very much....
  6. Apr 5, 2009 #5


    Staff: Mentor

    Yes, if dk/dy = 0, then k = a constant.
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