Upon completion of this unit, students will be able to explain and illustrate the connection between the early attempts to measure non-rectangular and curvilinear objects to the formal methods of elementary calculus. The contributions of various mathematicians will be integrated into the study of the mathematical concepts. Students should be able to describe social and political influences upon these mathematicians and how the times in which they lived impacted the development of the theorem. Through the use of specific examples, students will demonstrate their ability to apply the fundamental theorem of calculus.

Technology communication tools: Routinely and efficiently use online information resources to meet needs for collaboration, research, publications, communications, and productivity. Select and apply technology tools for research, information analysis, problem-solving, and decision-making in content learning.

Standard 2: Evaluates information critically and competently, as described by the following indicators: distinguishes among facts, point of view, and opinion; selects information appropriate to the problem or question at hand.

The fundamental theorem of calculus is one of three fundamental theorems in mathematics: of arithmetic, of algebra, and of calculus. Calculus is an intellectual creation which students can better appreciate when they understand the background of this theorem as well as know how to apply it.This unit endeavors to provide sufficient background knowledge to empower students to be both users of the application and adventurers in the development of new ideas.

Students should be able to apply the fundamental theorem of calculus and to explain its historical development. Calculations using paper and pencil, graphics calculators, or a website designed for this task, as well as oral and written expositions of the history and application of the Fundamental Theorem are appropriate.

1. History: People and Places Influencing the Fundamental Theorem of Calculus 2. The Definite Integral and Riemann Sums 3. The Fundamental Theorem of Calculus

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History: People and Places Influencing the Fundamental Theorem of Calculus