?(a) What is an oriented surface? Give an example of a nonorientable surface.(b) Define

Chapter 16, Problem 13

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QUESTION:

(a) What is an oriented surface? Give an example of a nonorientable surface.

(b) Define the surface integral (or flux) of a vector field F over an oriented surface S with unit normal vector n.

(c) How do you evaluate such an integral if S is a parametric surface given by a vector function r(u, v)?

(d) What if S is given by an equation z = g(x, y)?

Questions & Answers

QUESTION:

(a) What is an oriented surface? Give an example of a nonorientable surface.

(b) Define the surface integral (or flux) of a vector field F over an oriented surface S with unit normal vector n.

(c) How do you evaluate such an integral if S is a parametric surface given by a vector function r(u, v)?

(d) What if S is given by an equation z = g(x, y)?

ANSWER:

Step 1 of 5

Consider the given integral is,

                                       

 

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