Download Presentation
## MAT 1235 Calculus II

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**MAT 1235Calculus II**4.4 Part II Indefinite Integrals and the Net Change Theorem http://myhome.spu.edu/lauw**Homework**• WebAssign HW 4.4 II**Preview**• We will discuss the Net Change Theorem • The NCT explains the formulas for computing displacement and distance traveled you have learned in physics.**The Net Change Theorem**The integral of rate of change is the net change Final value –Initial Value = Net change of from to Rate of change of**Example 1**= volume of the solution in the tank at time t = rate of change of the volume**Example 2: Linear motion of a particle**Reference Frame**Recall: Section 2.7**• displacement ≠ distance traveled**displacement ≠ distance traveled**displacement = distance traveled =**Observations**distance traveled = displacement =**Observations**distance traveled = -displacement =**Observations: A Unified Formula**distance traveled = displacement = distance traveled = -displacement =**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**Example 3**Step 2: Use the distance formula**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.