Fundamental Theorem of Calculus (FTC)

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Bloom’s Taxonomy

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Bloom’s Taxonomy for different levels of understanding
Figure 1.1: Bloom's Taxonomy

Fundamental Theorem of Calculus

Theorem: Fundamental Theorem of Calculus - Part II (FTC-II)

Fundamental Theorem of Calculus - Part II: Let f(x) be continuous on [a,b] and F(x) any antiderivative of f(x), then

abf(x)dx=F(b)F(a).

Explanation of FTC-II

Conditions

There are two (2) condition(s), i.e., requirements, for this theorem:

Conclusion

If both conditions are true, then the conclusion (the statement after the word “then” in the theorem) is also true, i.e.,

abf(x)dx=F(b)F(a).

Interpretation of FTC-II

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Created: Tuesday, 25 August 2020 02:28 EDT Last Modified: Monday, 30 May 2022 - 13:58 (EDT)