(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi

First of all this a text book question from Stroud Advanced Engineering Mathematics, solution is given, but no steps are shown.

A question I just cant seem to solve at the moment, as below.

A function f(x) is defined by [tex]f(x) = \pi - x:0 < x < \pi[/tex]

[tex] f(x + 2\pi) = f(x)[/tex]

Express the function as a half range cosie series

2. Relevant equations

Im at a loss of how to start this question, Ive been doing fine when they havent included pi in the function itself.

I know as its wanted as a cosine series I'll have to make it resemble an even function and thus my a0 and an terms can be

[tex]2/\pi \int^{\pi}_{0}\pi - x dx[/tex]

[tex]\stackrel{2}{\pi}\int^{\pi}_{0}\pi - x\:cosnx:dx[/tex]

So my main question is really how I remove pi. Ive tried taking it out as a constant which doesnt work, so I have a feeling Im not realising something

The final solution according to the book is

[tex] \pi/2 + 4/\pi\left\{cosx + 1/9:cos3x + 1/25:cos5x+ ...\right\}[/tex]

I keep getting [tex] -\pi^2[/tex] for a0

Thank you for reading and any help

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# Homework Help: Fourier series (integration of pi)

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