Polydisperse granular flow has been extensively studied using kinetic theory, where approximations, such as the Taylor series expansion and/or neglect of the contribution of certain terms, were made to derive the constitutive relation due to the difficulties faced in the analytical integration related to pair distribution function. In this note, a new method was proposed to exactly calculate the integration related to pair distribution function without any approximations. It was found that different integration methods can result in several orders of magnitude difference of collision frequency, which highlights the importance of proper calculation of the integration related to pair distribution function in the derivation of constitutive relations. (c) 2020 Elsevier Ltd. All rights reserved.