ESE 2024Q6
Q: The temperature distribution T(x) at a distance x, measured from one end, along a bar of length L is given by T(x) = Kx(L − x) (0 ≤ x ≤ L), K = constant. A Fourier series expansion consisting of sine terms only for T(x) is
(a)(8KL²/π³) Σ_{n=1}^{∞} [1/(2n−1)³] sin((2n−1)πx/L)
(b)(8KL²/π³) Σ_{n=1}^{∞} [1/(2n−1)²] sin((2n−1)πx/L)
(c)(8KL³/π³) Σ_{n=1}^{∞} [1/(2n−1)³] sin((2n−1)πx/L)
(d)(8KL³/π³) Σ_{n=1}^{∞} [1/(2n−1)²] sin((2n−1)πx/L)
Answer pending verification