---
tags: mth201, dailyprep
---

# Daily Prep 10B -- MTH 201-04

## Overview

In Module 10A, we learned that we can estimate the distance traveled by a moving object with a known velocity, by estimating the area between its velocity curve and the horizontal axis. In Module 10B we introduce a systematic way to construct these estimates known as a **Riemann sum**. It's nothing mysterious --- just the method we saw of sticking rectangles under the curve and adding up their areas --- but it leads to a breakthrough in answering the "distance traveled" question that we'll encounter in Module 11.

## 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.

- Calculate a sum that's given in "sigma" notation.
- Estimate the area under a curve using a small number of rectangles whose heights are determined using left, right, and middle points.

**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.

- Explain the general process of setting up a Riemann sum.
- Calculate a simple left, right, and middle Riemann sum by hand.
- Determine whether a Riemann sum will be an overestimate or underestimate of the true area under a curve.
- Use a computer to set up and calculate a larger Riemann sum.

## Resources for learning

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

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

- Screencast 4.2.1 -- Quick review: Riemann sums (3:29) https://www.youtube.com/watch?v=oUZdflwDse0&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=79
- Screencast 4.2.2 -- Sigma notation (7:15) https://www.youtube.com/watch?v=Eq-DCz52Ozs&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=80
- Screencast 4.2.3 -- Computing a left-hand Riemann sum (8:55) https://www.youtube.com/watch?v=yVZX0YRRTvA&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=81
- Screencast 4.2.3(b) -- Another Riemann sum example (10:34) https://www.youtube.com/watch?v=FvhD3BblfvI&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=82
- Screencast 4.2.4 -- Calculating right and midpoint Riemann sums (9:33) https://www.youtube.com/watch?v=zl02nRV4Ui4&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=83

**Text:** In the _Active Calculus_ text, [read Section 4.2](https://activecalculus.org/single/sec-4-2-Riemann.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 ("MTH 201 Daily Prep 10B").

## 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.