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This Concept Map, created with IHMC CmapTools, has information related to: MATH_calculus4, INTEGRAL example: areas under/over a curve, infinitesimal CALCULUS discovered/ invented Gottfried Leibniz [1646-1716], INTEGRAL concepts include primitives, via 3 stages: . anticipation . development . rigorization 3rd stage, rigorization replaced infinitesimals with principle of limits, INTEGRAL studies accumulation of quantities, APPLICATIONS include . area between two curves . curve length . areas and volumes of revolution * . field Intensity, CALCULUS built upon two major ideas INTEGRAL, INTEGRAL concepts include anti-derivatives, example: areas under/over a curve, infinitesimal CALCULUS built upon the shoulders of ...., Gottfried Leibniz [1646-1716] developed infinitesimal calculus, INTEGRAL serves APPLICATIONS, limits concepts include real numbers, DIFFERENTIAL serves APPLICATIONS, INTEGRAL concepts include integrals, CALCULUS etymology Latin [calculus] = a small stone used for counting, limits concepts include derivatives, DIFFERENTIAL concepts include derivatives, CALCULUS built upon two major ideas DIFFERENTIAL, infinitesimal CALCULUS define infinitesimal: infinitely small numbers greater than zero