How to integrate Acos(wt + theta) ?

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Homework Help Overview

The discussion revolves around the integration of the function Acos(ωt + θ), where A represents amplitude, ω is angular velocity, and θ is a phase shift. Participants are exploring the integration process and the implications of the variables involved.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are considering the use of substitution methods for integration and questioning the variables with respect to which the integration should be performed. There is also discussion about the limits of integration and the nature of the function being integrated.

Discussion Status

The discussion is ongoing, with some participants suggesting substitution as a viable approach while others express uncertainty about the integration limits and the role of the variables. There is no explicit consensus on the method to be used, but guidance has been offered regarding the nature of the integral.

Contextual Notes

Participants are noting that the integration is to be performed with respect to time (t), treating ω and θ as constants during the process. There is also mention of the integral being evaluated over one period, which may influence the outcome.

Chandasouk
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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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With respect to theta? omega?
 
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:
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([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.
 
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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