AP Calculus

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Special Focus: The Fundamental Theorem of Calculus Here again, students may find it helpful to build a table of values to help them analyze function F 4 . Alternatively, teachers might choose to point out that since ⎧⎪ F2 ( x) for x < 0 F4 ( x) = ⎨ ⎩⎪ F( x) for x ≥ 0 f (| t|) = ⎧ ⎨ ⎩ f ( − t) for t < f ( t) for t ≥ Hence, the graph of F 4 is just the graph of F 2 combined with the graph of F. The graph of F 4 appears below. 0 0 . The graph of f (| t|) on [–4,4] (e) Finally, students should consider F5 ( x) = ∫ f ( t) dt. They should first 0 recognize that the graph of y = f ( t) is x The graph of f ( t) on [0,4] AP® Calculus: 2006–2007 Workshop Materials 53
Special Focus: The Fundamental Theorem of Calculus Students will find it helpful to build a table of values to help them analyze function F 5 . The graph of F 5 appears below. The graph of F 5 on [0,4] A Return to the Worksheet Once the antiderivative part of the Fundamental Theorem has been introduced, the class can return to this worksheet to probe further. The graph of f on [0,4] 54 AP® Calculus: 2006–2007 Workshop Materials
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AP Calculus

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