Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
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Calculus I
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Calculus II
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Calculus III

Course: Calculus II
Topic: Geometry
Subtopic: Net Change

Overview

Before delving into displacement, net change, and future position, it would be good to review Motion and the Derivative from Calculus I where we discussed position, velocity, and acceleration functions and how one is the derivative of another. In this section we build on those concepts and introduce a new(ish) interpretation of the integral. The net change of a function is the definite integral of its rate of change, basically the Fundamental Theorem of Calculus (FTC) in action.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 6.1.1 Understand that displacement is the change in position and when it is positive vs negative.
• 6.1.2 Understand the difference between displacement of and total distance traveled by a moving object and how to calculate each.
• 6.1.3 Given the velocity of a moving object, be able to set-up and use integrals to find position, displacement, and distance traveled.
• 6.1.4 Understand and be able to calculate net change, future value, and future position of a moving object given sufficient information about the object's position and/or velocity.

Terminology

Review: position, velocity, speed, acceleration

Terms you should be able to define: displacement, distance traveled, net change, future value, future position

TIP: Consider relationships between displacement and total distance versus net and total change versus velocity and speed.

 Displacement: net change in position = integral of velocity Distance traveled: total change in position = integral of speed

Text Notes

When studying section 6.1 of Calculus, Early Transcendentals (3rd ed) text by Briggs/Cochran/etc., please note this connection between FTC and three theorems. Important to understand!

Mini-Lectures and Examples

Supplemental Resources (recommended)

Video: Org. Chem Tutor's Net Change Theorem, Definite Integral, & Rates of Change Word Problems

There are two videos from Univ. of Austin Texas recommended in Mini-Lecture: applications of the net change theorem post in WAMAP, along with a part of the "Blood Flow" tutorial video that accompanies our textbook. That post includes some added explaination worth checking out.

rev. 2021-01-05