Chapter 14: Multiple Integration
- Page ID
- 25103
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- 14.1: Prelude to Multiple Integration
- In this chapter we extend the concept of a definite integral of a single variable to double and triple integrals of functions of two and three variables, respectively. We examine applications involving integration to compute volumes, masses, and centroids of more general regions. We will also see how the use of other coordinate systems (such as polar, cylindrical, and spherical coordinates) makes it simpler to compute multiple integrals over some types of regions and functions.
- 14.2: Double Integrals over Rectangular Regions
- In this section we investigate double integrals and show how we can use them to find the volume of a solid over a rectangular region in the xy-plane.
- 14.3: Double Integrals over General Regions
- In this section we consider double integrals of functions defined over a general bounded region D on the plane.
- 14.4: Double Integrals in Polar Coordinates
- Double integrals are sometimes much easier to evaluate if we change rectangular coordinates to polar coordinates.
- 15.E: Multiple Integration Exercises for Study
- Exercises for self-study and review of multiple integration, taken verbatim from OpenStax Calculus Volume 3.