- #1
castusalbuscor
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Homework Statement
So I have to find the Fourier series for [tex]sin^{5}(x)[/tex].
Homework Equations
I know the [tex]a_{n}[/tex] in:
[tex]\frac{a_{0}}{2} + \sum^{\infty}_{n=1}a_{n}cos_{n}x + \sum^{\infty}_{n=1}b_{n}sin_{n}x[/tex]
goes to zero, which leaves me with taking the [tex]b_{n}[/tex].
The Attempt at a Solution
So what I got so far is trying to integrate to find [tex]b_{n}[/tex].
[tex]b_{n} = \frac{1}{\pi} \int^{\pi}_{-\pi} sin^{5}(x)sin(nx)[/tex]
But I am not sure how to proceed from here, do I make use of [tex]sin^{2}(x)=1/2(1-cos2x)[/tex] and [tex]cos^{2}(x)=1/2(1+sin2x)[/tex]?
Am I even going in the right direction?edit:
I just plugged it into Maple and got:
[tex]\frac{1}{\pi}\left( \frac{sin((n-5)x}{32(n-5)} - \frac{sin((n+5)x}{32(n+5)} - \frac{5sin((n-3)x}{32(n-3)} + \frac{5sin((n-1)x}{16(n-1)} - \frac{5sin((n+1)x}{16(n+1)} \right)^{\pi}_{-\pi}[/tex]
is this the direction I need to go in?
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