How to integrate Acos(wt + theta) ?

  • Thread starter Chandasouk
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  • #1
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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?
 

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  • #2
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With respect to theta? omega?
 
  • #3
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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:
  • #4
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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.
 
  • #5
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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

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.
 
  • #6
HallsofIvy
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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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