Fourier Series for Periodic Functions - Self Study Problem

[Gopal Mailpalli]

Self Study
1. Homework Statement
Consider a periodic function f (x), with periodicity 2π,

Homework Equations

$A_{0} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)dx$
$A_{n} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)cos\frac{2\pi rx}{L}dx$
$B_{n} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)sin\frac{2\pi rx}{L}dx$

The Attempt at a Solution

$A_{0} = C$
$A_{n} = 0$
$B_{n} = \frac{-C}{\pi r}cos\pi r$
http://imgur.com/a/4Q2oL

 

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Your

Self Study
1. Homework Statement
Consider a periodic function f (x), with periodicity 2π,

Homework Equations

$A_{0} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)dx$
$A_{n} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)cos\frac{2\pi rx}{L}dx$
$B_{n} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)sin\frac{2\pi rx}{L}dx$

The Attempt at a Solution

$A_{0} = C$
$A_{n} = 0$
$B_{n} = \frac{-C}{\pi r}cos\pi r$
http://imgur.com/a/4Q2oL

This post should have been sent to Calculus and Beyond Forum.

Your picture is hardly readable. Better to type the text in, or write it clearly and make a better picture.
The formula for the b coefficients is not correct. What happens in case of even index? What is b₂, for example?