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Chapter 14: Q.no1TF (page 1142)

Generalizing to Higher Dimensions: Stokes' Theorem is about a surface inside of鈩�3. But the essence of the theorem has to do with integrating over a surface, and does not use any properties that 鈩�3 has which 鈩�4 does not.

How would a version of Stokes' Theorem for role="math" localid="1650715550032" 鈩�4 need to change to accommodate the extra dimension?

Short Answer

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A version of Stokes' Theorem for need to change to accommodate the extra dimension

Step by step solution

01

Introduction

A version of Stokes' Theorem for need to change to accommodate the extra dimension

02

Introduction

The essence of the theorem has to do with integrating over a surface

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Most popular questions from this chapter

Find the masses of the lamina:

The lamina occupies the region of the hyperboloid with equation z2+4=x2+y2 that lies above and/or below the disk of radius 5 about the origin in the XY-plane, and the density function, 蟻(x, y,z), is proportional to the distance from the origin.

What is the difference between the graphs of

G(x,y)=xi+yjandF(x,y)=鈭�xi+(-y)j

Give an example of a field with positive divergence at (1, 0, 蟺).

Evaluate the integrals in Exercises 43鈥�46 directly or using Green鈥檚 Theorem.

鈭�R3xy-4x2ydA, where R is the unit disk.

ComputethedivergenceofthevectorfieldsinExercises17鈥�22.G(x,y,z)=(x2+y鈭�z)i鈭�2ycoszj+ex2+y2+z2k
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