Applications of Integration

Start with an overview

Begin with the mind maps titled Applications of Integration. They outline areas between curves and several ways to find volumes, including disks, washers and known cross-sections. Use an overview to see the terms and steps before moving to a specific example.

The maps include steps for finding area, such as graphing functions and finding intersection points. As you study, follow those steps in the map and explain how they relate to the area between the curves.

Explore volume and mean value

After the overview, open Calculus Notes for the shell method of finding the volume of solids of revolution. Compare it with the disk, washer and cross-section approaches named in the overview maps. Pay attention to how each resource describes the volume calculation.

The flashcards Mean Value of functions ask how to calculate a function’s mean value and include a worked example. Use them after the maps to practice another application of integration and check the calculation shown.

Study the examples

The collection also includes mind maps with examples involving electric current, production cost, a lifted bucket and a braking car. Pick an example and identify the quantity described in the problem. Then follow the integration work shown in the resource.

These examples give university students a way to practice reading an application alongside the broader maps. Teachers can use the same resources when looking for material on particular applications.

Connect your study

Applications of Integration is a section of the Integration unit in Mathematics. Use the overview maps to keep the section’s area and volume methods in view as you work through the notes and examples.

There are no quizzes on this page. Instead, pair a mind map with the mean-value flashcards: study the map, then use the cards for practice. Explore a map and a flashcard deck to get started.