Fourier Transform: Solving f(x) Homework Statement

[phrygian]

Homework Statement

f(x) = {-1, -pi<x<0 ; 1, 0<x<pi ; 0, |x|>pi}

Find the exponential Fourier transform of the given f(x) and write f(x) as a Fourier integral.

Homework Equations

The Attempt at a Solution

I have the equations for the Fourier transforms and I know how to find the Fourier series for f(x) but I have no idea where to start this one, my book is very confusing. Can someone help me start this?

 

[vela]

What is the definition of the Fourier transform you are using?

 

[HallsofIvy]

The Fourier transform I am familar with is
$$\frac{1}{\sqrt{2\pi}}\int_{x=-\infty}^\infty f(x)e^{-isx}dx$$
If that is what you know, just go ahead and do the integration:
$$\frac{1}{\sqrt{2\pi}}\left(-\int_{-\pi}^0 e^{-isx}dx+ \int_0^\pi e^{-isx}dx\right)$$