6
$\begingroup$

Can anyone help me to prove that these integral inequalities hold?

Here $x$ is a real value:

$$ \left| \int_a^b\ f(x) dx \right| \leq \int_a^b\ |f(x)| dx $$

Here $z$ is a complex value:

$$ \left| \int_C^ \ f(z) dz \right| \leq \int_C^\ |f(z)| |dz| $$

  • 0
    What is $|dz|$?2012-10-26
  • 0
    @Did For a contour integral around a path $\gamma(t)$, $|dz|$ is a shorthand for $|\gamma'(t)| dt$2013-06-12
  • 2
    @user71815 Thanks, I know. My goal with this comment was to help the OP to precise the setting of their question (but, as you can see, the OP was not interested in that).2013-06-12

4 Answers 4