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.