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Calculus III (Practice Problems) / Surface Integrals / Stokes' Theorem   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Practice Problems
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Surface Integrals of Vector Fields Previous Section   Next Section Divergence Theorem

 

1. Use Stokes’ Theorem to evaluate  where  and S is the portion of the sphere of radius 4 with  and the upwards orientation.  [Solution]

 

2. Use Stokes’ Theorem to evaluate  where  and S is the portion of   in front of  with orientation in the negative x-axis direction.  [Solution]

 

3. Use Stokes’ Theorem to evaluate  where  and C is is the circle of radius 3 at  and perpendicular to the y-axis.  C has a clockwise rotation if you are looking down the y-axis from the positive y-axis to the negative y-axis.  See the figure below for a sketch of the curve.

 

[Solution]

 

4. Use Stokes’ Theorem to evaluate  where  and C is is triangle with vertices ,  and C has a counter clockwise rotation if you are above the triangle and looking down towards the xy-plane.  See the figure below for a sketch of the curve.

[Solution]

 

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Surface Integrals of Vector Fields Previous Section   Next Section Divergence Theorem
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Calculus III (Practice Problems) / Surface Integrals / Stokes' Theorem    [Notes] [Practice Problems] [Assignment Problems]

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