4.4 to 4.6

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AP Calculus Test: The FTC & Numeric Integration (Calculators only permitted on #10 & #11)

1. Evaluate .

2. Evaluate .

3. Evaluate .

4. Evaluate .

5. Evaluate .

6. Evaluate .

7. Determine the average value of  on the interval .

8. Find , given that

9. Use the definition of the definite integral (the limit process) to evaluate .

Graph of

10. The graph of a differentiable function on  is shown above. The graph of consists of three line segments, a quarter circle and a semicircle. Let  be a function given by .

1. Evaluate , , and.
2. Determine the interval(s) on which  is increasing. Justify your answer.
3. Determine the interval(s) on which  is concave down. Justify your answer.
4. Find the absolute maximum value of on the interval . Justify your answer.

11. Use a Trapezoidal Sum of 4 subintervals of equal width to estimate .

12. Solve the differential equation below to find , given that :

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Last modified: 01/09/08