ยง6.1: Areas Between Curves
In this section, we extend definite integrals to find the area bounded by two functions. Key strategies include choosing the correct variable of integration ($dx$ vs $dy$) and identifying intersection points.
Library, Handouts & Tools
| Resource Name | Type | Description | Link |
|---|---|---|---|
| Interactive Area Visualizer | Desmos Tool | Dynamic graph showing area as "Top minus Bottom" with adjustable bounds. | Launch App |
| Paul's Notes: Area Between Curves | Study Guide | Comprehensive guide covering both $dx$ and $dy$ integration methods. | Read Notes |
| Paul's Notes: Practice Problems | Problem Set | A variety of problems requiring you to find intersection points and determine the correct integration orientation ($dx$ vs $dy$). | View Problems |
| Practice Problems | Handout | Collection of standard problems with solution keys. | Download PDF |
Video Lectures
| Topic | Source | Description | Link |
|---|---|---|---|
| Areas Between Curves | Univ. of Houston | Standard lecture covering the setup of integrals for area between two graphs. | Watch |
| Introduction & Basic Examples | Professor Dave | Visual explanation of subtracting integrals to find the enclosed area. | Watch |
| Integrating with Respect to y | Houston Math Prep | Crucial technique: Using "Right minus Left" functions ($x=f(y)$) for simpler integration. | Watch |