Riemann Sums & Definite Integrals
David Brown
6 min read
Listen to this study note
Study Guide Overview
This study guide covers accumulation of change, its connection to graphs (area under the curve), and the use of definite integrals. It explains how the sign of the rate of change affects accumulation, and how to determine the units of accumulated change. It also provides a worked example and practice questions, along with a glossary of key terms like boundary value.
#Accumulation of Change
#Table of Contents
- Introduction to Accumulation of Change
- Connection with Graphs
- Sign of Rate of Change
- Units of Accumulation of Change
- Worked Example
- Practice Questions
- Glossary
- Summary and Key Takeaways
#Introduction to Accumulation of Change
#What is an Accumulation of Change?
An accumulation of change refers to the total change in a quantity over a given interval, based on its rate of change.
If you know the rate of change of a quantity, then an accumulation of change is the actual change that occurs to the quantity over a specified interval.
For example, if a strawberry harvester gathers 0.5 kilograms of strawberries for each meter of strawberry plants (rate of change = 0.5 kilograms per meter), then over 6 meters, the accumulation of change is:
To find a total value for the quantity, a boundary value (a known value at a specific point) is required. For instance, if 23 kilograms of strawberries have already been harvested, after another 6 meters of harvesting:
#Connection with Graphs
#Graph...
How are we doing?
Give us your feedback and let us know how we can improve