Troubleshooting Fourier & TI-89 Integration

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SUMMARY

The discussion focuses on troubleshooting integration of Fourier series expressions using the TI-89 calculator. The specific integral evaluated is 2∫(1-x)sin(nωx)dx, which yields an incorrect result when n is included in the sine and cosine functions. The user suspects that the TI-89 may not recognize 'n' as a variable, leading to discrepancies in the output. The conversation highlights the importance of specifying variable types in symbolic computation tools like TI-89 and Maple.

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I'm currently working with Fourier-series and have to integrate some expressions, like this one:

[tex]2\int_{0}^{1} (1-x)*sin(n \omega x) dx = 2 \left[- \frac{1}{n \pi}(1-x) cos(n \pi x) - \frac{1}{(n \pi)^2} sin(n \pi x) \right]_{0}^{1} = \frac{2}{n \pi}[/tex]

Trying to evaluate this (with [tex]\omega = \pi[/tex])on the TI-89 does not give this result. And the thing is that if I remove the n from the sine and cosine expressions, then the answer comes out right. Why is this? Should I assume the n is 1 in the sine and cosine functions in the square parentheses?
 
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i don't think I've used one of those calculators before but maybe it doesn't know what n is. (real, complex, integer, a variable like x, y, z, etc etc) i don't think maple always knows either. sometimes it gives the most general answer possible & i have to tell it to give me a positive integer, or it just spits out the same thing i typed in because i wasn't specific enough with what i wanted it to do.
 

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