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Homework Help: How to integrate Acos(wt + theta) ?

  1. Sep 3, 2010 #1
    How do you integrate Acos([tex]\omega[/tex]t + [tex]\theta[/tex]) ? Where A is the amplitude, omega is angular velocity, and theta is position? I have no idea what to do. Should I U substitute?
  2. jcsd
  3. Sep 3, 2010 #2
    With respect to theta? omega?
  4. Sep 3, 2010 #3
    I'm actually not sure, the integral is being taken from 0 to T and the equation is Acos([tex]\omega[/tex]t + [tex]\theta[/tex])dt
    Last edited: Sep 3, 2010
  5. Sep 3, 2010 #4
    Yes, you can U substitute.
    Or ask yourself what is the derivative of sin(wt+theta).

    If the capital T is period(as usual), you don't need to actually integrate it and write down 0 as the answer. Because there is no DC content in a sinusoid.
  6. Sep 3, 2010 #5


    Staff: Mentor

    That dt tells you that integration is to be done with respect to t, so as far as the integration is concerned, t is the variable and the other two are just constants.
  7. Sep 4, 2010 #6


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    Science Advisor

    You would be able to integrate [itex]\int cos(x) dx[/itex] wouldn't you? So it is just that [itex]\omega t+ \theta[/itex] that is the problem.

    So let [itex]u= \omega t+ \theta[/itex].
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