Troubleshooting Fourier & TI-89 Integration

[TSN79]

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

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

Trying to evaluate this (with $$\omega = \pi$$)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?

 

[fourier jr]

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.

 

[ravenprp]

First of all, great job on working with Fourier-series and integrating expressions! It can definitely be a tricky topic, but it seems like you have a good grasp on it.

Regarding your question about the discrepancy in the results between keeping and removing the "n" in the sine and cosine expressions, I would recommend checking your calculator settings. The TI-89 has a setting called "Exact/Approx" which can affect the way it evaluates certain expressions. If this setting is set to "Approx," it may be rounding off the values and causing the discrepancy in your results.

Additionally, it is important to keep in mind that the "n" in the sine and cosine expressions does not necessarily have to be equal to 1. It can be any integer, and it is typically used to represent the different harmonics in a Fourier-series. So, you should not assume that it is equal to 1 in this case.

If adjusting your calculator settings does not solve the issue, I would recommend double-checking your calculations and possibly seeking assistance from a math tutor or professor. Sometimes, a fresh set of eyes can help catch any errors or misunderstandings.

I hope this helps and good luck with your Fourier-series and integration!