Abstract—This paper presents a simpler and shorter method of evaluating integrals of powers of sine. The reduction formula for sine is repeatedly applied to the integral of the nth power of sine until generalized formulas are derived. Since the derivation process involves recursive relations, the coefficients and exponents of the derived formulas showed certain patterns and sequences which were used as the basis for developing an easier algorithm.

Index Terms—Integration, mathematical algorithm, powers of sine, reduction formula, trigonometric identities.

Lito E. Suello is with Malayan Colleges Laguna, Pulo-Diezmo Road, Cabuyao City, Laguna, Philippines (email: lesuello@mcl.edu.ph).

Cite: Lito E. Suello, "Simplified Method of Evaluating Integrals of Powers of Sine Using Reduction Formula as Mathematical Algorithm," International Journal of Applied Physics and Mathematics vol. 5, no. 3, pp. 192-198, 2015.