1. If the following functions represent the derivative of the original function, find the original function. Antiderivative – If F’(x) = f(x) on an interval, then F(x) is the antiderivative of f(x) for every value of x on the interval. 4.1 – Antidifferentiation

2. State the derivative of each function. 4.1 – Antidifferentiation

3. Rules of Antidifferentiation Properties of Antidifferentiation

4. Write the antiderivative of each of the following functions. 4.1 – Antidifferentiation

5. Write the antiderivative of each of the following functions. 4.1 – Antidifferentiation

6. Write the antiderivative the following function. 4.1 – Antidifferentiation

7. Initial Condition Problems 4.1 – Antidifferentiation

8. Initial Condition Problems 4.1 – Antidifferentiation

9. Applications 4.1 – Antidifferentiation a)

10. Applications 4.1 – Antidifferentiation b)

11. Applications 4.1 – Antidifferentiation c) d)

12. Applications 4.1 – Antidifferentiation e) f)

13. Area Under a Curve 4.2 – Antiderivatives as Areas A particle travels at a velocity of 8 feet per second. What is the total distance traveled in 3 seconds? The area below the graph of a function and above the x-axis has meaning depending on the use of the function.

14. Area Under a Curve 4.2 – Antiderivatives as Areas

15. Sequence – a function whose domain is positive integers. Sigma Notation – A mathematical notation that represents the sum of many terms using a formula. 4.2 – Antiderivatives as Areas

16. Examples Sigma Notation 4.2 – Antiderivatives as Areas

17. Express the sums in sigma notation. Sigma Notation 4.2 – Antiderivatives as Areas

18. Estimating Area Under a Curve Left-hand endpoints 1 2 4.2 – Antiderivatives as Areas

19. Estimating Area Under a Curve Left-hand endpoints 1 2 4.2 – Antiderivatives as Areas

20. Estimating Area Under a Curve Left-hand endpoints 1 2 4.2 – Antiderivatives as Areas