# Thread: Two integrals I encountered in fourier analys

1. ## Two integrals I encountered in fourier analysis

(1)

$u(t)=\left\{\begin{array}{ccc}2,&0\leq t < 1\\1, & 1 \leq t < 2\\0, & 2 \leq t < 3\end{array}\right.$

$\frac{1}{3}\int_{0}^{3}u(t)e^{-in\frac{2\pi}{3}t}dt, n = 0,1,2,...$

(2)

$\frac{1}{\pi}\int_0^{\pi} |\cos t|e^{-i2nt}dt$

I know some rules about odd and even functions but I can't seem to apply them here.

2. For both of those integrals, you'll need to break up the region of integration so that you can write a more explicit formula for u(t).

3. I can solve the integrals, but the answer I'm getting is too complex (no pun intended heh). The answer is supposed to be fourier coefficients that I need to generalize for different values of n, and I don't see how I can get my answer to be what the textbook says.

4. Ok: what answer are you getting? And what is the book's answer?