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CSS Applied Mathematics QUESTION #4161
Question 1
In the Fourier series $f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty}[a_n\cos(nx) + b_n\sin(nx)]$, what is $a_0$ for $f(x) = x$ on $[-\pi, \pi]$?
  • $0$✔️
  • $\pi$
  • $2\pi$
  • $\frac{\pi}{2}$
Correct Answer Explanation
$a_0 = \frac{1}{\pi}\int_{-\pi}^{\pi} x \, dx = 0$ since $x$ is an odd function integrated over symmetric interval.