Question

Any idea how to evaluate
pi/2 int_{0}^{infty}i ^{(ix)} dx ?

Answer 1

The integral I'm looking for is: \[\pi/2 \int\limits_{0}^{\infty}i ^{(ix)} dx\]

Answer 2

just notice \(\huge i=e^{\frac{\pi}{2}i} \)

Answer 3

Thanks mukushla, I then get \[i^{(ix)} = e^{(\pi/2)x i^2} = e^{-(\pi/2)x} \]

Answer 4

yep; exactly

Answer 5

This integral looks a lot easier to solve :)