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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 spherical

coordinates?

Short Answer

Expert verified

dV=ρ2sinϕdρdθdϕ

Step by step solution

01

Given Information

The given dVis volume increment.

The spherical coordinates areρ,θ,ϕ

02

Simplification

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

Mathematically,

f(ρ,θ,ϕ)dV=f(ρ,θ,ϕ)ρ2sinϕdρdθdϕ

Comparing we get

dV=ρ2sinϕdρdθdϕ

This is becauseρis expressed as a function of θand 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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