Find the Fourier Transform of $f(x)$, given that $f(x) = |x|$ if $-1

Question

I'm doing some general practice questions on Fourier Transform from my book. Came across this one and don't know from where to begin. How do I put the absolute value of $x$ in the integral for the Fourier transform? Please help.

Answer 1

Here is a start

$$\int_{-\infty}^{\infty} f(x)e^{-ixw} dx = \int_{-1}^{1} |x| e^{-ixw}dx$$

Now, you need to split the interval $[-1,1]$ and use the definition of the abosolut value to evaluate the later integral.