On some class of oscillating integrals / M. Sh. Shikhsadilov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 4. P. 55-57 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 191-192].

The following result is proved in the paper: if for some real A>0 and some natural number n>1 for all x from [0,1] we have the inequality |f^{(n)}(x)|\geq A, then the following estimate is valid:

|I|=\left|\int_0^1\limits\rho(f(x))\;dx\right|\leq\min{\{1;4nA^{-1/n}\}}, where \rho(t)=0,5-\{t\}.

Key words: "saw-tooth" function, trigonometric integrals.

№ 4/2015