This course completion paper aims to apply the composite Simpson's rule (RSC) adapted to a numerical solution of a double integral called Simpson's double integral (IDS), in order to ratify an alternative present in the literature. to obtain the solution of a double integral. In this sense, a brief review of the concepts regarding the functions of two variables was presented, addressing limit and continuity, followed by the theory concerning double integrals, as well as the concept of interpolation, in particular Lagrange interpolation, which served theoretical support to define simple and compound Simpson's rules, with the composite adapted to estimate the solution of a double integral considering a non-rectangular integration region. An application was developed, where it consisted of solving a double integral that determined the volume of a solid comprised between two paraboloids. This integral was calculated analytically as well as numerically having the results compared through the relative error. Such comparison ratified that the numerical strategy approached presents itself as an attractive alternative mainly in the impossibility of determining the value of a double integral analytically.
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