AP Calculus

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Special Focus: The Fundamental Theorem of Calculus The Integral Function—Class Worksheet Benita Albert Oak Ridge High School Oak Ridge, Tennessee The graph of the function y=f(t) is shown below. The function is defined for 0 ≤ t ≤ 4 and has the following properties: • The graph of f has odd symmetry around the point (2,0). • On the interval [0,2], the graph of f is symmetric with respect to the line t=1. 1 4 • ∫ f ( t) dt = . 0 3 Graph of y=f(t) AP® Calculus: 2006–2007 Workshop Materials 33
Special Focus: The Fundamental Theorem of Calculus 1. Let F( x) = ∫ f ( t) dt . 0 x a. Complete the following table of values. x 0 1 2 3 4 F(x) b. Sketch your best estimate of the graph of F on the grid below. y = F( x) 34 AP® Calculus: 2006–2007 Workshop Materials
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AP Calculus

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