Final answer:
To find the first four non-zero terms in the Fourier series expansion for a piecewise function, determine the coefficients of the sine and cosine functions by evaluating integrals. Then, use these coefficients to write the non-zero terms of the series.
Step-by-step explanation:
The Fourier series expansion for the piecewise function f(x) can be found by first determining the coefficients of the sine functions in the expansion. Since the function is defined in the interval [-π, π], the coefficients can be calculated using the following formulas:
a0 = (1/π) ∫ f(x) dx
an = (1/π) ∫ f(x) sin(nx) dx
bn = (1/π) ∫ f(x) cos(nx) dx
To find the first four non-zero terms, we need to calculate the values of a0, a1, b1, a2, and b2.
By substituting the function f(x) into the above formulas and evaluating the integrals, we can find the coefficients. Finally, using these coefficients, we can write the first four non-zero terms of the Fourier series expansion for f(x).