On some improper integrals containing products between the tails of Maclaurin series for the sine and cosine functions

Abstract

The values of twenty-six improper integrals containing products between the tails of Maclaurin series for the sine and cosine functions are evaluated using elementary methods. The values found extend work where the values for six improper integrals containing the squares of the tails of the Maclaurin series for the sine and cosine functions were recently reported.