SECTION 5.4 The Fundamental Theorem of Calculus. Basically, (definite) integration and differentiation are inverse operations.

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Presentation transcript:

SECTION 5.4 The Fundamental Theorem of Calculus

Basically, (definite) integration and differentiation are inverse operations.

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

The Mean Value Theorem for Integrals We know the area of a region under a curve is greater than the area of an inscribed rectangle, & 2. less than the area of a circumscribed rectangle. The MVT states that there exists some rectangle “between” those with area equal to the area of the region under the curve.

The Mean Value Theorem for Integrals (cont.)

Average Value of a Function

Example 9

Second Fundamental Theorem

Example 10