Asymptotic areas between powers of sine and cosine curves

Atiratch Laoharenoo, Chanatip Sujsuntinukul

Motivated by Dombrowski and Dresden's work in 2025, we find the exact values of the limits \[\lim_{k\to\infty}\int_0^{ρπ}|\sin^n(kx)-\sin^nx|dx\quad\text{and}\quad \lim_{k\to\infty…