I am studying Fourier for an exam and came across something in my notes that I can't get my head round, might be a simple integration issue. Let me explain.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

The tutorial question in my notes that I am studying is as following:

1. Consider the periodic function defined by f(t) = {[tex]\frac{-1 \ \ \ \ -\pi \leq t \leq 0}{1 \ \ \ \ 0 < t < \pi}[/tex]

Find its Fourier expansion.

2. Relevant equations

a_{0}= 0 (because odd function)

a_{n}= 0 (because odd function)

b_{n}= [tex]\frac{2}{\pi} \int^{\pi}_{0} f(t) \ sin \ nt \ dt[/tex]

3. The Solution written on my notes:

b_{n}= [tex]\frac{2}{\pi} \int^{\pi}_{0} 1 \ sin \ nt \ dt[/tex]

b_{n}= [tex]\frac{2}{\pi} \left[-\frac{1}{n} \ cos \ nt\right]^{\pi}_{0}[/tex]

My question is, how can you get [tex]-\frac{1}{n} \ cos \ nt [/tex] when integrating [tex] 1 \ sin \ nt[/tex].

Should it not have been [tex]t \ cos \ nt[/tex] if integrating with respect to t (dt)?

I know it might be a simple answer but I have been studying for a while now and can't get my head round this, are my notes incorrect?

Note: I have it worked out in my notes down to the solution where [tex] f(t) = \frac{4}{\pi}(sint+\frac{1}{3}sin3t+\frac{1}{5}sin5t+\frac{1}{7}sin7t+...)[/tex] I have omitted most of the working out and most of my notes as they are irrelevant to my question.

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# Homework Help: Fourier Integration

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