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Chapter 13: Q 13. (page 1066)

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

Expert verified

The six forms are dxdydz,dxdzdy, dydxdz, dydzdx, dzdxdy, dzdydx.

Step by step solution

01

Given Information

It is given that we need to evaluatedVin rectangular system as triple integral.

02

Simplification

Let x,y,zbe the coordinates in rectangular coordinate system.

Let dx,dy,dzbe small increment.

The volume in rectangular coordinates is given by dV=dxdydz

The six forms used to express the volume increment dVwill be dxdydz,dxdzdy,dydxdz,dydzdx,dzdydx,dzdxdy.

The shape of region determines the order of integration.

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