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Basic Trig Integral Question. 
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#1
Apr912, 02:07 AM

P: 446

1. The problem statement, all variables and given/known data
This question is part of Fourier Series in Circuit Analysis. There were fairly straightforward integrals which I calculated and confirmed using MAPLE to be correct, however the book gives somewhat different answers. I would presume that what I did was correct and the solutions manual made an error, however since it's a fairly large question with answers being carried forward I want to make doubly sure. Sorry about the size of the images, I will remove them after the problem This is the integral essentially, the definite integral from 2 to 4 is left out because it's zero, f(t) = 5 for 0 < t < 1 f(t) = 10 for 1 < t < 2 2. Relevant equations cos (Pi/2) = (1)[itex]^{\frac{n1}{2}}[/itex] cos (Pi) = (1)[itex]^{n}[/itex] 3. The attempt at a solution My answer came to this: EDIT: cos(nPi/2) goes to (1)^n/2  still doesn't reconcile my answers with the book though. The MAPLE output was: [itex]5\,{\frac {1+\cos \left( 1/2\,n\pi \right) 2\,\cos \left( n\pi \right) }{n\pi }}[/itex] The answer in the book was (last line before the table): As you can imagine, because the answers are different, the values in the table are going to be different and hence whatever I have to plot afterwards will be different. 


#2
Apr912, 09:45 AM

Mentor
P: 11,685

##(1)^{integer}## cannot produce any zeros, it can only produce +1 or 1. So it doesn't replace ##cos(n \pi / 2)##.



#3
Apr912, 10:29 AM

P: 446

I should have been clearer, cos (n*Pi/2) is replaced by (1)^n/2
So if n = 3, I'm guessing that term is ignored because you can't compute that. At least that's the identity they gave in the book. 


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