Exact value of integrals involving product of sine or cosine function

Authors

  • Ratinan Boonklurb Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Thailand
  • Atiratch Laoharenoo Department of Mathematics and Computer Science, Kamnoetvidya Science Academy, Rayong 21210, Thailand

DOI:

https://doi.org/10.53733/235

Keywords:

product of sine integral, product of difference of cosine integral, integer sequence

Abstract

By considering the number of all choices of signs $+$ and $-$ such that $\pm \alpha_1 \pm \alpha_2 \pm \alpha_3 \cdots \pm \alpha_n = 0$ and the number of sign $-$ appeared therein, this paper can give the exact value of $\int_{0}^{2\pi} \prod_{k=1}^{n} \sin (\alpha_k x) dx$. In addition, without using the Fourier transformation technique, we can also find the exact value of $\int_{0}^{\infty}\frac{(\cos\alpha x - \cos\beta x)^p}{x^q} dx$. These two integrals are motivated by the work of Andrican and Bragdasar in 2021, Andria and Tomescu in 2002, and Borwein and Borwein in 2001, respectively.

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Author Biographies

Ratinan Boonklurb, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Thailand

Department of Mathematics and Computer Science
Faculty of Science, \\ Chulalongkorn University
Bangkok 10330
Thailand
ratinan.b@chula.ac.th

Atiratch Laoharenoo, Department of Mathematics and Computer Science, Kamnoetvidya Science Academy, Rayong 21210, Thailand

Atiratch Laoharenoo
Department of Mathematics and Computer Science
Kamnoetvidya Science Academy
Rayong 21210
Thailand
atiratch.l@kvis.ac.th

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Published

12-10-2022

How to Cite

Boonklurb, R., & Laoharenoo, A. . (2022). Exact value of integrals involving product of sine or cosine function. New Zealand Journal of Mathematics, 53, 51–61. https://doi.org/10.53733/235

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