How to integrate Acos(wt + theta) ?

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The discussion focuses on integrating the function Acos(ωt + θ) with respect to time (t), where A is the amplitude, ω is the angular velocity, and θ is the phase position. Participants confirm that a U-substitution is appropriate, specifically using u = ωt + θ, to simplify the integration process. It is emphasized that since the integral is taken over one period (0 to T), the result will be zero due to the absence of DC content in a sinusoidal function. The integration is straightforward once the substitution is made, as it reduces to integrating cos(u).

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How do you integrate Acos(\omegat + \theta) ? 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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With respect to theta? omega?
 
I'm actually not sure, the integral is being taken from 0 to T and the equation is Acos(\omegat + \theta)dt
 
Last edited:
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.
 
Chandasouk said:
I'm actually not sure, the integral is being taken from 0 to T and the equation is Acos(\omegat + \theta)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.
 
You would be able to integrate \int cos(x) dx wouldn't you? So it is just that \omega t+ \theta that is the problem.

So let u= \omega t+ \theta.
 

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