Question

Write the Euler constants ao, an and bn of the Fourier series of the
function f(x) in(0,3).​

Answer 1

Answer:

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• Force is push or pull acting on a body which tends to change its state of rest or of motion.
• It is denoted by "F".

Answer 2

Concept:

A Fourier series is a sum of sine and cosine waves that represents a periodic function. Each wave in the sum, or harmonic, has a frequency that is an integer multiple of the fundamental frequency of the periodic function. Harmonic analysis may be used to identify the phase and amplitude of each harmonic.

Given:

The coefficients $a_0, a_n$ and $b_n$.

Find:

The value of the coefficient of the Fourier series.

Solution:

The coefficients of the Fourier series are,

$a_0 = \frac{1}{T} \int\limits^T_0 {f(x)} \, dx \\a_n = \frac{2}{T} \int\limits^T_0 {f(x)cos(\frac{2\pi nx}{T}) } \, dx \\b_n = \frac{2}{T} \int\limits^T_0 {f(x)sin(\frac{2\pi nx}{T}) } \, dx$

Hence, the value of coefficients is given.