Abstract: Based on the residue theorem and the so-called Jordan＇s lemma, a new lemma is proposed to treat integrals along an arc of infinitely increasing radius. A modified approach is suggested to evaluate infinite integrals involving sine and cosine functions. Some illustrative examples are given and thus the effectivity and simplicity of this approach are shown.

Key words: infinite integrals involving sine and cosine functions, analytic functions, contour integration, residue theorem