Chapter 13: Q 13. (page 1066)

What are the six forms used to express the volume increment $d V$ when you use rectangular coordinates to evaluate a triple integral? How do you decide which order to use?

Short Answer

Expert verified

The six forms are $d x d y d z,$ $d x d z d y$ , $d y d x d z$ , $d y d z d x$ , $d z d x d y$ , $d z d y d x$ .

Step by step solution

Given Information

It is given that we need to evaluate $d V$ in rectangular system as triple integral.

Simplification

Let $(x, y, z)$ be the coordinates in rectangular coordinate system.

Let $d x, d y, d z$ be small increment.

The volume in rectangular coordinates is given by $d V = d x d y d z$

The six forms used to express the volume increment $d V$ will be $d x d y d z, d x d z d y, d y d x d z, d y d z d x, d z d y d x, d z d x d y$ .

The shape of region determines the order of integration.

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What are the six forms used to express the volume increment $d V$ when you use rectangular coordinates to evaluate a triple integral? How do you decide which order to use?

Short Answer

Step by step solution

Given Information

Simplification

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What are the six forms used to express the volume increment dVwhen you use rectangular coordinates to evaluate a triple integral? How do you decide which order to use?

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

Probability and Statistics

Logic and Functions

Pure Maths

Calculus

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

What are the six forms used to express the volume increment $d V$ when you use rectangular coordinates to evaluate a triple integral? How do you decide which order to use?