MAT 1235 Calculus II 4.4 Part II Indefinite Integrals and the Net Change Theorem

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Presentation transcript:

MAT 1235 Calculus II 4.4 Part II Indefinite Integrals and the Net Change Theorem

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.

Recall: Fundamental Theorem of Calculus Part 2

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

Example 1: Solution leaking from a tank

Example 1

Example 2: Linear motion of a particle Reference Frame

Example 2:

Formulas

Recall: Section 2.7 displacement ≠ distance traveled

displacement = distance traveled =

Observations distance traveled = displacement =

Observations distance traveled = -displacement =

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

Formulas

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.