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Suppose f(x, y, z)=\frac{1}{\sqrt {x^{2} + y^{2} +z^{2}}} and W is the bottom half of a sphere of...

Question:

Suppose {eq}f(x, y, z)=\frac{1}{\sqrt {x^{2} + y^{2} +z^{2}}} {/eq} and W is the bottom half of a sphere of radius 3. Enter {eq}\rho {/eq} as rho {eq}\phi {/eq} as phi, and {eq}\theta {/eq} as theta. As a elated integral {eq}\int \int \oint_{w} f d v = \oint^{B}_{A} \oint^{D}_{C} \oint^{F}_{E} \: d \rho \ d \pi \ d \theta {/eq} with limits of integration

A.=

B.=

C.=

D.=

E.=

F. =

Evaluate the integral.

Spherical Coordinates:

The spherical coordinates are especially useful when we calculate the integral for spheres centered on the origin.

In this case, all integration variables vary between constant values.

Answer and Explanation: 1

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Taking into account the set can be expressed in spherical coordinates as:

{eq}W:\left\{ {\begin{array}{*{20}{c}} {0 \leqslant \rho \leqslant 3}...

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Cylindrical & Spherical Coordinates: Definition, Equations & Examples

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Chapter 13 / Lesson 10
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In this lesson, we introduce two coordinate systems that are useful alternatives to Cartesian coordinates in three dimensions. Both cylindrical and spherical coordinates use angles to specify the locations of points, a feature they share with 2-D polar coordinates.


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