1. 4035 Functions Defined by the Definite Integral
BC 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) = 12
TI-89 Graph then F-5 Math #7
TI nd 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 $ and deposit $20.00 a week for 4 weeks.
My brother has $ 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 ProblemsIf
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. If F( 1) = -2 find 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
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