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The full range is 
(length 
), so the half range is 
. The half range sine series would then be given by
where
Essentially, this is the same as finding the Fourier series for the function
Integrating by parts yields
So the half range sine series for this function is simply
where
Essentially, this is the same as finding the Fourier series for the function
Integrating by parts yields
So the half range sine series for this function is simply