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Chapter 14: Q. 3 (page 1149)

Does the divergence theorem apply to the surface that are not closed

Short Answer

Expert verified

No the divergence theorem is not applied to the surface that are not closed.

Step by step solution

01

Given information

We are given a surface that is not closed

02

Explaination

No divergence theorem is not applied to the surface that are not closed. The divergence theorem states that the surface integral of the normal component of a vector point function “F” over a closed surface “S” is equal to the volume integral of the divergence of F. Hence the surface must be closed.

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Most popular questions from this chapter

Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) Two different surfaces with the same area. (Try to make these very different, not just shifted copies of each other.)

(b) Let S be the surface parametrized by r(u,z)=x(u,z)i+y(u,v)j+z(u,v)k.

Give two different unit normal vectors to S at the point r(u0,v0).

(c) A smooth surface that can be smoothly parametrized as r(x,z)=x,f(x),z.

Find the areas of the given surfaces in Exercises 21–26.

S is the lower branch of the hyperboloid of two sheets z2=x2+y2+1that lies below the annulus determined by 1≤r≤2 in the xy plane.

Evaluate the integrals in Exercises 43–46 directly or using Green’s Theorem.

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

In what way is Green’s Theorem a special case of Stokes’ Theorem?

ComputethedivergenceofthevectorfieldsinExercises17–22.F(x,y,z)=xeyzi+yexzj+zexyk
See all solutions

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