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SECTION 5.4
The Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus
• 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
•
Example 5
•
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Example 6
•
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.)
Average Value of a Function
•
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Example 9
•
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Second Fundamental Theorem
Example 10
•
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