Introduction

class="introduction"

class="key-equations" title="Key Equations"

class="key-concepts" title="Key Concepts"

class="review-exercises" title="Review Exercises"

class="practice-test" title="Practice Test"

class="try"

class="checkpoint"

class="section-exercises"

A photo of a glass ovoid dome reflecting in the water to make something like a football shape.

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. As an example, we will use polar coordinates to find the volume of structures such as l’Hemisfèric. (See [link].)

In the preceding chapter, we discussed differential calculus with multiple independent variables. Now we examine integral calculus in multiple dimensions. Just as a partial derivative allows us to differentiate a function with respect to one variable while holding the other variables constant, we will see that an iterated integral allows us to integrate a function with respect to one variable while holding the other variables constant.

This work is licensed under a Creative Commons Attribution 4.0 International License.

You can also download for free at http://cnx.org/contents/9a1df55a-b167-4736-b5ad-15d996704270@5.1

Attribution:

For questions regarding this license, please contact partners@openstaxcollege.org.
If you use this textbook as a bibliographic reference, then you should cite it as follows: OpenStax College, Calculus. OpenStax CNX. http://cnx.org/contents/9a1df55a-b167-4736-b5ad-15d996704270@5.1.
If you redistribute this textbook in a print format, then you must include on every physical page the following attribution: "Download for free at http://cnx.org/contents/9a1df55a-b167-4736-b5ad-15d996704270@5.1."
If you redistribute part of this textbook, then you must retain in every digital format page view (including but not limited to EPUB, PDF, and HTML) and on every physical printed page the following attribution: "Download for free at http://cnx.org/contents/9a1df55a-b167-4736-b5ad-15d996704270@5.1."