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CSS Applied Mathematics QUESTION #4157
Question 1
For the Fourier series of an even function $f(x)$ on $[-L, L]$, which coefficients are zero?
  • All $a_n$
  • All $b_n$✔️
  • All $a_n$ and $b_n$
  • None
Correct Answer Explanation
For even functions, $f(-x) = f(x)$, so $b_n = \frac{1}{L}\int_{-L}^{L} f(x)\sin(\frac{n\pi x}{L})dx = 0$ since integrand is odd. Only cosine terms ($a_n$) remain.