Question: Consider the function (f(x)= begin{cases}0 & text { if }-1 leq x leq 0, 2 & text { if } 0 leq x leq

Consider the function $f(x)= \begin{cases}0 & \text { if }-1 \leq x \leq 0, \\ 2 & \text { if } 0 \leq x \leq 1\end{cases}$

Calculate the first two terms of the Fourier-Legendre series of $f(x)$ over the interval $-1 \leq x \leq 1$. What is the value of the complete Fourier-Legendre series of $f(x)$ at $x=0$ ?

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