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Chapter 13: Q 15. (page 1066)

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=蚁2sin蠒d蚁d胃d蠒

Step by step solution

01

Given Information

The given dVis volume increment.

The spherical coordinates are蚁,胃,蠒

02

Simplification

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

Mathematically,

鈭�鈭�鈭�f(蚁,胃,蠒)dV=鈭�鈭�鈭�f(蚁,胃,蠒)蚁2sin蠒d蚁d胃d蠒

Comparing we get

dV=蚁2sin蠒d蚁d胃d蠒

This is because蚁is expressed as a function of 胃and 蠒, it gives the simplest order of integration.

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

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