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Exploring the Fundamental Theorem of Calculus

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Resource Type: Demonstration, GeoGebra, Proof

A two part GeoGebra exploration of the area of the curve under a function (step by step details for teacher demonstration or student exploration), followed  by a simplified version of a proof of the FTC, designed for *intuitive* understanding. This resource has been developed and refined over many years while teaching students  years, aimed at helping students gain deep understanding of the FTC, without overwhelming them with too much notation. In my experience, this makes a good opening sequence for the Integration topic, then do a few weeks work of using the FTC, then go back and revisit this work again. The FTC is a classic example of where several iterative loops of alternately focusing on concepts and skills strengths understanding. In truth, deep understanding of the FTC only happens for most us after many years of exposure.

20 January 2021 Edit: 20 January 2021

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Topics:
AdvancedCalculusIntegration
Resource Type:
DemonstrationGeoGebraProof
Australian Curriculum / Mathematical Methods:
Unit 3 Topic 2 IntegralsFundamental theorem
NSW Mathematics Advanced Stage 6 Syllabus:
CalculusMA-C4 Integral CalculusC4.2 Areas and the definite integral

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