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Let be $f:\mathbb{R}\rightarrow \mathbb{C}$. This $$\operatorname{Re} \int_a^b {{e^{ - i\theta }}f(x)dx = } \int_a^b {\operatorname{Re} ({e^{ - i\theta }}f(x))dx}$$

is True? Why?

  • 1
    What is your definition of $\int_a^b f(x)\,dx$ for a complex-valued $f$?2012-10-29
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    $\int_a^b f(x)\,dx$ is real number2012-10-29
  • 0
    That can't be right - what is $\int_0^1 i\,dx$ then?2012-10-29
  • 0
    mmmm understand2012-10-29

1 Answers 1