Section: Engineering Mathematics | Marks: 2
Common Data: Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^2$ for $-\pi \le x \le \pi$ and $f(x + 2\pi) = f(x)$. The Fourier series of $f$ in $[-\pi, \pi]$ is
- A. $\frac{\pi^2}{3} + 4\sum_{n=1}^\infty \frac{\cos nx}{n^2}$
- B. $\frac{\pi^2}{3} + \sum_{n=1}^\infty \frac{(-1)^n \cos nx}{n^2}$
- C. $\frac{\pi^2}{3} + 4\sum_{n=1}^\infty \frac{(-1)^n \cos nx}{n^2}$
- D. $\frac{\pi^2}{3} + \sum_{n=1}^\infty \frac{\cos nx}{n^2}$