Intgration of a harmonic function

[lordcx]

intgration of a function*** help please***

I found this explanation in a journal paper but I could not understand it. Can someone give me an explanation or possibly a proof that


if:

then why integration over whole period is:

I have problem with the power of omega, my solution returns w with power 2, while the power of omega in answer is one, Can someone help me for the reason?

I appreciate your helps.

 

[jvicens]

Hello,

I can definitely help you with your question about integration of a function. First, let's define some terms. Integration is a mathematical operation that calculates the area under a curve. This is often used in physics and engineering to calculate quantities such as displacement, velocity, and acceleration.

The notation you have provided is commonly used to represent the integration of a function, where f(t) is the function being integrated and the limits of integration are from t=0 to t=T. This means that you are calculating the area under the curve of f(t) from t=0 to t=T.

Now, to address your question about the power of omega. In this context, omega (ω) represents the angular frequency of the function f(t). The power of omega in the answer is one because the function f(t) is being integrated over a whole period, which is equivalent to integrating from 0 to 2π (since one period is equal to 2π radians). Therefore, the power of omega is one because it is being raised to the power of one (ω^1).

I hope this explanation helps you understand the concept of integration and the power of omega in this context. If you have any further questions, please let me know.