why is this integral zero

[tommycashmoney]

i don't understand why this integral is zero


i understand that if w = 0, the value is zero, but if w = infinite, i can't see how it makes zero e^-2inifnite * e^i(T)(infinite)

 

[LCKurtz]

In the numerator you have [MATH]\omega e^{-i\omega t} e^{-2\omega}[/MATH]. Note that [MATH]|e^{i\theta}| =1[/MATH] for any [MATH]\theta[/MATH].

 

[tommycashmoney]

In the numerator you have [MATH]\omega e^{-i\omega t} e^{-2\omega}[/MATH]. Note that [MATH]|e^{i\theta}| =1[/MATH] for any [MATH]\theta[/MATH].

Okay, ans why do we consider only the absolute value? And even if it is 1, how does it make zero in the end?

 

[Deleted member 4993]

Okay, ans why do we consider only the absolute value? And even if it is 1, how does it make zero in the end?

in this case || does not indicate absolute value - it indicates "magnitude" (which is always "positive" like || - but different consequences).

\(\displaystyle \left| e^{it}\right| \ = \ \left| cos(t) \ + \ i \cdot sin(t) \right| \ \ = 1\)

 

[LCKurtz]

Okay, ans why do we consider only the absolute value? And even if it is 1, how does it make zero in the end?

With [MATH]t> 0[/MATH], what happens to [MATH]\omega e^{-\omega t}[/MATH] as [MATH]\omega \to \infty[/MATH]?