How to integrate Acos(wt + theta) ?

[Chandasouk]

How do you integrate Acos($$\omega$$t + $$\theta$$) ? Where A is the amplitude, omega is angular velocity, and theta is position? I have no idea what to do. Should I U substitute?

 

[mg0stisha]

With respect to theta? omega?

 

[Chandasouk]

I'm actually not sure, the integral is being taken from 0 to T and the equation is Acos($$\omega$$t + $$\theta$$)dt

 

[klondike]

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.

 

[Mark44]

I'm actually not sure, the integral is being taken from 0 to T and the equation is Acos($$\omega$$t + $$\theta$$)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.

 

[HallsofIvy]

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 $u= \omega t+ \theta$.