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6 035 Functions Defined by the Definite Integral

6 035 Functions Defined by the Definite Integral. AB Calculus. Accumulation Functions. BIG PICTURE:. Given Then A (x) is the Accumulation function . The points on A(x) reflects the amount under the curve f (t). Net Area: Net Distance Net Money:.

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6 035 Functions Defined by the Definite Integral

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  1. 6035 Functions Defined by the Definite Integral AB Calculus

  2. Accumulation Functions BIG PICTURE: Given Then A (x) is the Accumulation function. The points on A(x) reflects the amount under the curve f (t). Net Area: Net Distance Net Money:

  3. Functions Defined by the Definite Integral f (t) Also can work with negative accumulation. A (-1) = A (-2) =

  4. Functions Defined by the Definite Integral f (t) A (0) = A (1) = A (2) = A(3) = 0 12 TI-89 Graph then F-5 Math #7 TI-83 2nd Calc #7

  5. Functions Defined by the Definite Integral f (t) Also can work with negative accumulation. A (-1) = A (-2) =

  6. Functions Defined by the Definite Integral f (t) A (x) A (x) points indicate the quantity of accumulation under f (t).

  7. Verify: Write the equation A(x) = = A (0) = , A (1) = , A (2) = , A(3) = , A (-1)= , A (-2) =

  8. Writing the Equations: Initial Values = Particular Solutions REM: The Antiderivative finds… What do -2, 0, and 1 represent?

  9. Writing the Equations: Initial Values = Particular Solutions Example:

  10. Initial Value Problems : 1st Fundamental Theorem Think: I have $200.00 and deposit $20.00 a week for 4 weeks. My brother has $350.00 and deposits $20.00 a week for 4 weeks. or Words:

  11. Initial Value Problems (concept) If If A (0) = 4 , Find A (7) 4 + 4

  12. Initial Value Problems If If A (5) = 6 , Find A (8)

  13. Accumulation Functions The graph the derivative, f / ,is given. Suppose f (1) = 10. Find f (3) Suppose f (0) = 0. Find f (1), f (2), f (3)

  14. Accumulation Functions The graph of a function, f , is shown. a. Evaluate b. Determine the average value of the function on the interval [ 1 , 7 ]. c. IfF( 1) = -2find F ( 7). d. Determine the answers to parts a, b and c if the graph is translated two units up.

  15. AP type

  16. Last Update: • 01/30/10 • Get Text problems

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