James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

15
Multiple Integrals
Tumors, like the one shown,
have been modeled as
“bumpy spheres.” In Exercise
47 in Section 15.8 you are
asked to compute the volume
enclosed by such a surface.
© Juan Gaertner / Shutterstock.com
In this chapter we extend the idea of a definite integral to double and triple integrals of
functions of two or three variables. These ideas are then used to compute volumes, masses, and
centroids of more general regions than we were able to consider in Chapters 6 and 8. We also use
double integrals to calculate probabilities when two random variables are involved.
We will see that polar coordinates are useful in computing double integrals over some types
of regions. In a similar way, we will introduce two new coordinate systems in three-dimensional
space––cylindrical coordinates and spherical coordinates––that greatly simplify the computation
of triple integrals over certain commonly occurring solid regions.
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