The present work refers to the presentation and comparison of the numerical methods, Simpson's rule, compound and adaptive, in the resolution of an integral. In this context, the concepts of interpolation, truncation error and adaptive quadrature were presented, being implemented in the matlab interface, algorithms of the conventional Simpson type and adapted, in that order, to assist in the calculations. Thus, the result of a non-contextualized definite integral was displayed, which initially had its solution provided through the computational mechanism called Wolfram|Alpha. Afterwards, the integral was resolved by numerical means, granting a quantitative analysis using the theoretical foundation of the relative error, which indicated for the analyzed scenario that the adaptive Simpson's rule is more efficient both in accuracy and in convergence to less than one tolerance required.
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