Answered: b) f (x) — x(2 — х), 0 <х<2. = X f(x) f…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Need help with attached fourier series, I did a_0 and I belive its and odd function so their wont be any a_n in series but not sure, polease help

b) f (x) — x(2 — х), 0 <х<2.
= X
f(x)
f (x) 3 2х — х?,
0 < x < 2

Expert Solution

Solution:

Here, the function is even about x = 1.

So, obtain the constants $a_{0} and a_{n}$ :

$a_{0} = \frac{4}{3}$

$\begin{array}{rcl} a_{n} & = & \int_{0}^{2} (2 x - x^{2}) \cos (nπx) d x \\ = & \frac{2}{π^{2} n^{2}} \cos (2 π n) - \frac{2}{π^{2} n^{2}} - \frac{4}{π^{2} n^{2}} \cos (2 π n) + \frac{2}{π^{3} n^{3}} \sin (2 π n) \\ = & - \frac{4}{π^{2} n^{2}} \end{array}$

Step by step

Solved in 2 steps

Knowledge Booster

$Fourier Transformation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions