# 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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View this answerTaking 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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Chapter 13 / Lesson 10In 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.