---
tags: mth201, dailyprep
---

# Daily Prep 11A -- MTH 201-04

## Overview

In Module 11 we formally introduce the last Big Idea of MTH 201: The **definite integral** of a function on an interval. The definite integral (or just "integral") of a function is to finding area what the derivative of a function is to finding slopes --- it's a generic idea that expresses many of the concepts we saw in Module 10 regarding area under a curve, total distance traveled, and so on. In Module 11A we will introduce the idea and make sense of the notation used, and look at basic ways to calculate definite integrals and interpret the results.

## 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 definition of the **definite integral of a function** on an interval, and explain the meaning of each part of the notation.
- Explain what the definite integral of a function on an interval tells you, in terms of area and the graph of the function.
- Evaluate a definite integral exactly by interpreting it as an area, if the function given is made of lines and/or circles.

**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.

+ Use the Properties of the Definite Integral to compute, manipulate, and simplify definite integrals.
+ Calculate the average value of a function on an interval.

## Resources for learning

**I recommend watching the videos first for this Module.**

**Video:** Watch these at the GVSUMath YouTube playlist:

- Screencast 4.3.1 -- Quick review: The definite integral (3:01) https://www.youtube.com/watch?v=Lp5KsXN4UOQ&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=84
- Screencast 4.3.2 -- Calculating a definite integral using geometry (6:47) https://www.youtube.com/watch?v=oHIH69Ou4DE&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=85
- Screencast 4.3.3 -- Evaluating definite integrals using integral properties (8:15) https://www.youtube.com/watch?v=1SqpYAAyBCk&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=86
- Screencast 4.3.4 -- Average value of a function (7:35) https://www.youtube.com/watch?v=MQG9Nur4fdM&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=87

**Text:** In the _Active Calculus_ text, [read Section 4.3](https://activecalculus.org/single/sec-4-3-definite-integral.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 11A".

## 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.