Fundamental Theorem and Area


The Fundamental Theorem of Calculus links the derivative, the anti-derivative, and the concept of accumulation. The Fundamental Theorem can be used for area, volume, and accumulation problems.

Fundamental Theorem: Part 1


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Example Problem Set






Fundamental Theorem: Part 2


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Example Problem Set




Area


An important application of the Fundamental Theorem of Calculus is area calculations.

Example Problem Set





Final Problems



Problem 1


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a) -3 b) -2 c) 2 d) 3 e) 18


Problem 2



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Problem 3


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Answers



1. (d)
2. 0
3. 5.333 (to three places after the decimal which is the AP approved level of exactness)

Links


http://archives.math.utk.edu/visual.calculus/5/area2curves.2/index.html
http://www.sosmath.com/calculus/integ/integ03/integ03.html