Answer :

Solution :

f(t) is an even periodic function, Since

f(-t) = f(t)

The constant term in the Fourier series is: a_o/2

$a_o=\frac{1}{l}{\int }_{-l}^{l}f(t)dx$

l = 1

$a_o=\frac{1}{1}{\int }_{-1}^{1}f(t)dx$

Since the function is not continious, we need to break the integral according to interval

from -1 to 0, f(t) = 0,

from 0 to 1, f(t) = 4

$a_o={\int }_{-1}^{0}0dx+{\int }_0^{1}4dx$

The constant term is :

$\frac{a_o}{2}$ = 4/2 = 2