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, [itex]\int Re(f)dt= \int f(t)dt[/itex], then, yes, that is the same as [itex]Re \int f(t)+ g(t)i dt[/itex] because that last integer is [itex]\int f(t)dt+ i\int g(t)dt[/itex].

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

eliotsbowe

thanks a lot!