Chapter 5: Applications of Integration
Section 5.1 - Area of a Plane Region
Section 5.2 - Volume of a Solid of Revolution
Section 5.3 - Volume by Slicing
Section 5.4 - Arc Length
Section 5.5 - Surface Area of a Surface of Revolution
Section 5.6 - Differential Equations
Section 5.7 - Centroids
Section 5.8 - Work
Section 5.9 - Hydrostatic Force
Introduction
Integration is a summative process, with small bits being added up to make a whole. The small bits could be bits of area, volume, moments, work, or force. In the sections of this chapter, different applications of integration are examined as illustrations of the scope and utility of this part of the calculus. The actual integrations that need to be carried out are not demanding, and Maple can be a great help in separating out the details of the model from the details of the integration. Experience shows that more often then not, the issues that arise in a section on applications of integration are the details of the application, not the ensuing integration.
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