1. MAT 1235 Calculus II 4.4 Part II Indefinite Integrals and the Net Change Theorem http://myhome.spu.edu/lauw

2. Homework WebAssign HW 4.4 II

3. Preview We will discuss the Net Change Theorem The NCT explains the formulas for computing displacement and distance traveled you have learned in physics.

4. Recall: Fundamental Theorem of Calculus Part 2

7. The Net Change Theorem The integral of rate of change is the net change

8. Example 1: Solution leaking from a tank

9. Example 1

10. Example 2: Linear motion of a particle Reference Frame

11. Example 2:

12. Formulas

13. Recall: Section 2.7 displacement ≠ distance traveled

14. displacement = distance traveled =

15. Observations distance traveled = displacement =

16. Observations distance traveled = -displacement =

17. Observations: A Unified Formula distance traveled = displacement = distance traveled = -displacement =

18. Formulas

19. Example 3 The velocity function (in meters per second) is given for a particle moving along a line. (a) Find the displacement of the particle. (b) Find the distance traveled. Step 1: Find the interval where v(t)>0 and <0

20. Example 3 Step 2: Use the distance formula

21. Expectations Please pay attention to the solutions steps. Do not skip steps. Do not do multiple things at one step. It is very helpful to have a diagram.