Verify that the Stokes' theorem is true for the given vector field

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This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated.

Homework Statement



Verify that the Stokes' theorem is true for the vector field F(x,y,z) = -2yzi + yj + 3xk , S is the part of the paraboloid z = 2 - x2 - y2 that lies above the plane z = 1 oriented upward. (a) write the theorem (2 points); (b) LHS (4 Points ) (c) RHS (4 points)

Homework Equations



(a) ∫C F *dot* dr = ∫∫ScurlF *dot* dS

The Attempt at a Solution



(b) and (c) I really don't know where to start.
 

Answers and Replies

  • #2
Dick
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This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated.

Homework Statement



Verify that the Stokes' theorem is true for the vector field F(x,y,z) = -2yzi + yj + 3xk , S is the part of the paraboloid z = 2 - x2 - y2 that lies above the plane z = 1 oriented upward. (a) write the theorem (2 points); (b) LHS (4 Points ) (c) RHS (4 points)

Homework Equations



(a) ∫C F *dot* dr = ∫∫ScurlF *dot* dS

The Attempt at a Solution



(b) and (c) I really don't know where to start.

Not knowing even where to start is not good. That means you don't know how to use Stokes theorem at all. Try looking here. http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx If you have specific questions, post back.
 

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