@article{tjant2016465,
author={Lima, F. M. S.},
title={Evaluation of Some Non-trivial Integrals from Finite Products and Sums},
journal={Turkish Journal of Analysis and Number Theory},
volume={4},
number={6},
pages={172--176},
year={2016},
url={http://pubs.sciepub.com/tjant/4/6/5},
issn={2333-1232},
abstract={In this note, by manipulating the sums obtained from certain finite products of trigonometric functions at rational multiples of <span style="font-family:Times New Roman; font-size:16px;">&#960;</span>, I put them in the form of Riemann sums. By taking the limit as the number of (equally-spaced) subintervals tends to infinity, I have found exact closed-form results for some non-trivial integrals, e.g. <img src=image/abs1.png></img> <img src=image/abs2.png></img> <img src=image/abs3.png></img> and <img src=image/abs4.png></img> I also show how the method applies for the prompt evaluation of more complex integrals, such as <img src=image/abs5.png></img> <img src=image/abs6.png></img> <img src=image/abs7.png></img> <img src=image/abs8.png></img> <img src=image/abs9.png></img> and <img src=image/abs10.png></img> Since this approach does not involve any search for primitives, it can be a good alternative to more complex integration techniques.},
doi={10.12691/tjant-4-6-5}
publisher={Science and Education Publishing}
}