   Chapter 15, Problem 9RCC

Chapter
Section
Textbook Problem

(a) How do you change from rectangular coordinates to cylindrical coordinates in a triple integral?(b) How do you change from rectangular coordinates to spherical coordinates in a triple integral?(c) In what situations would you change to cylindrical or spherical coordinates?

(a)

To determine

To explain: How to change rectangular coordinates to cylindrical coordinates in a triple integral.

Explanation

The rectangular coordinates (x,y,z) corresponding to the cylindrical coordinates (r,θ,z) is,

x=rcosθy=rsinθz=z

Substitute x=rcosθ ,y=rsinθ and z=z in the given problem to convert rectangular coordinates into cylindrical coordinates. Thus, the integral becomes as given below.

If f is a cylindrical region E given by h1(θ)rh2(θ),αθβ, u1(rcosθ,rsinθ)zu1(rcos

(b)

To determine

To explain: How to change rectangular coordinates to spherical coordinates in a triple integral.

(c)

To determine

To explain: The reason to change from cylindrical coordinate system to spherical coordinate system or vice versa.

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