Intgration of a harmonic function help please

[lordcx]

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

actually this is not a homework, 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:

Homework Statement

if:

then why integration over whole period is:

Homework Equations

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?

 

[dextercioby]

Well, when you do a change of variable in the integral in the LHS, one omega pops up in the denominator, canceling one of the 2 from the numerator. That's why the RHS contains omega only to the power 1.

 

[lordcx]

Well, when you do a change of variable in the integral in the LHS, one omega pops up in the denominator, canceling one of the 2 from the numerator. That's why the RHS contains omega only to the power 1.

thank you, but as you see cos(hwt) contains both h and w. means by changing the variable the power of w and h should be equal. I'm confused

and over whole period:

then we will have

not

am I wrong??