---
# System prepended metadata

title: Daily Prep 12B -- MTH 201-04
tags: [' dailyprep', mth201]

---

---
tags: mth201, dailyprep
---

# Daily Prep 12B -- MTH 201-04

## Overview 

Our last Daily Prep of the semester! And in this lesson, we'll work with one last important result that connects definite integrals and the FTC to everyday life -- the **Total Change Theorem**, which tells us that the integral of a rate of change gives a total change. 

## Learning objectives 

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. 

+ State the Total Change Theorem. 
+ Explain how a definite integral can be used to solve a problem about total change.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. 

+ Find the total amount of change in a function on an interval, using a definite integral. 



## Resources for learning

**Video:** Just one video this time: 

- Screencast 4.4.4 -- Application of the Total Change Theorem (6:41) https://www.youtube.com/watch?v=Q8ZKTA4w9q0&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=91

**Text:** Re-read [the section on the Total Change Theorem in Section 4.4 in the Active Calculus text](https://activecalculus.org/single/sec-4-4-FTC.html). 

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises 

The exercises for this Daily Prep are found on student.desmos.com. Look for "MTH 201 Daily Prep 12B".


## Submission and grading 

**Submitting your work:** Just work through the activities; your work is saved as you go. 

**How this is graded:** Daily Prep assignments are graded on the basis of *completeness and effort*: If your submission has **all parts completed** (no blank entries, even if left blank accidentally) and **a good-faith effort to provide a correct solution or explanation is given** (no responses of "I don't know" or "I didn't understand") and **the work is submitted on time**, it gets a "check". Otherwise it gets an "x". If you are stuck on an item, you're expected to ask questions and give your best effort.  