?If is a constant vector, , and is an oriented, smooth surface with a simple, closed

Chapter 16, Problem 41

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QUESTION:

If  is a constant vector, , and  is an oriented, smooth surface with a simple, closed, smooth, positively oriented boundary curve , show that

                        

Questions & Answers

QUESTION:

If  is a constant vector, , and  is an oriented, smooth surface with a simple, closed, smooth, positively oriented boundary curve , show that

                        

ANSWER:

Step 1 of 3

Suppose is a constant vector, and S is an oriented, smooth surface with a simple, closed, smooth, positively oriented boundary curve C.

To prove that

Let us consider

By Stoke’s theorem, we know that

We will prove that

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