Chapter 13: Q 15. (page 1066)

The volume increment $d V = - - -$ when you use spherical coordinates to evaluate a triple integral. Why is this the standard order of integration for spherical
coordinates?

Short Answer

Expert verified

$d V = ρ^{2} \sin ϕ d ρ d θ d ϕ$

Step by step solution

Given Information

The given $d V$ is volume increment.

The spherical coordinates are $(ρ, θ, ϕ)$

Simplification

We need to solve it using spherical coordinates to evaluate triple integral.

Mathematically,

$\int \int \int f (ρ, θ, ϕ) d V = \int \int \int f (ρ, θ, ϕ) ρ^{2} \sin ϕ d ρ d θ d ϕ$

Comparing we get

$d V = ρ^{2} \sin ϕ d ρ d θ d ϕ$

This is because $ρ$ is expressed as a function of $θ$ and $ϕ$ , it gives the simplest order of integration.

That is why this is the standard order of integration for spherical coordinates.

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The volume increment $d V = - - -$ when you use spherical coordinates to evaluate a triple integral. Why is this the standard order of integration for spherical
coordinates?

Short Answer

Step by step solution

Given Information

Simplification

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The volume incrementdV=--- when you use spherical coordinates to evaluate a triple integral. Why is this the standard order of integration for sphericalcoordinates?

Short Answer

Step by step solution

Given Information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Geometry

Discrete Mathematics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

The volume increment $d V = - - -$ when you use spherical coordinates to evaluate a triple integral. Why is this the standard order of integration for spherical
coordinates?