Re{} and Im{} operators under the integral sign

[eliotsbowe]

Hello, I'm trying to figure out what hypothesis I need to swap the Re{} (or Im) operator and the integral sign, but I can't find anything on the matter. I guess either it's a trivial question or a rare one. Can someone help me?

Thanks in advance.

 

[Dickfore]

is the dummy variable real or complex?

 

[HallsofIvy]

If your complex function is f(t)+ g(t)i where t is a real variable, and the integral is, say, $\int Re(f)dt= \int f(t)dt$, then, yes, that is the same as $Re \int f(t)+ g(t)i dt$ because that last integer is $\int f(t)dt+ i\int g(t)dt$.

If, however, f is a complex function of a complex variable that is not necessarily true.

 

[eliotsbowe]

thanks a lot!