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SECTION 5.4 The Fundamental Theorem of Calculus
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Basically, (definite) integration and differentiation are inverse operations.
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Example 1
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Example 2
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Example 3
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Example 4
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Example 5
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Example 6
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Example 7
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Example 8
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The Mean Value Theorem for Integrals We know the area of a region under a curve is... 1. 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.
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The Mean Value Theorem for Integrals (cont.)
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Average Value of a Function
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Example 9
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Second Fundamental Theorem
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Example 10
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