TY - JOUR
AU - Boonklurb, Ratinan
AU - Laoharenoo, Atiratch
PY - 2022/10/12
Y2 - 2022/12/08
TI - Exact value of integrals involving product of sine or cosine function
JF - New Zealand Journal of Mathematics
JA - NZ J Math
VL - 53
IS -
SE - Articles
DO - 10.53733/235
UR - https://nzjmath.org/index.php/NZJMATH/article/view/235
SP - 51--61
AB - <p>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.</p>
ER -