The calculation of the moment of inertia of an extended body, as presented in standard introductory-level textbooks, involves the evaluation of a definite integral--an operation often not fully mastered by beginners, let alone the conceptual difficulties it presents, even to the advanced student, in understanding and setting up the integral in the first place. We here use dimensional analysis along with elementary differentiation techniques to derive the moments of inertia of various extended bodies. The suggested method does not employ integrals and, in effect, is just a disguised application of elementary ordinary differential equations.