Functions Defined by Integrals

1. Functions Defined by Integrals Day 1

2. The Definite Integral as a Number Constant Constant f is a function of x

3. The Definite Integral as a Function of x F is a function of x f is a function of t Constant

4. 1. A function g is defined on the interval [0, 6] by • where f is the function graphed on the next slide. Fill in the following table of values.

5. 0 ½ 1 ½ 0 ½ 1

6. 2.Let • where f is the function graphed on the next slide. Fill in the following table of values.

7. 0 2 7 5 2

8. 3.Let • where f is the function graphed on the next slide. Fill in the following table of values.

9. HW: Worksheet - 0   − 1  − ½

10. Day 2

11. 4. Use the Fundamental Theorem of Calculus to rewrite the following accumulation functions. Then find the derivative of each function.

14. The Second Fundamental Theorem of Calculus

16. Second Fundamental Theorem of Calculus (Chain Rule Version)

18. 7. Use the Second Fundamental Theorem to evaluate:

20. 8. The graph of a function f consists of a quarter circle and line segments. Let g be the function given by