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Calculus III (Assignment Problems) / Surface Integrals / Surface Integrals of Vector Fields   [Notes] [Practice Problems] [Assignment Problems]

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Paul
August 7, 2018


Calculus III - Assignment Problems
Line Integrals Previous Chapter  
Surface Integrals Previous Section   Next Section Stokes' Theorem

 Surface Integrals of Vector Fields

 

1. Evaluate  where  and S is the portion of  that is in the 1st octant oriented in the positive z-axis direction. 

 

2. Evaluate  where  and S is the portion of  that lies in front of  oriented in the negative x-axis direction.

 

3. Evaluate  where  and S is the portion of  that lies over the region in the xz-plane with bounded by ,  and the x-axis oriented in the positive y-axis direction. 

 

4. Evaluate  where  and S is the portion of  between  and  oriented outward (i.e. away from the z-axis). 

 

5. Evaluate  where  and S is the portion of  with  oriented outwards (i.e. away from the origin).

 

6. Evaluate  where  and S is the portion of  between  and  oriented inward (i.e. towards from the y-axis).

 

7. Evaluate  where  and S is the surface of the solid bounded by  and  with the negative orientation.  Note that both surfaces of this solid are included in S.

 

8. Evaluate  where  and S is the surface of the solid bounded by , , and  with the positive orientation.  Note that all three surfaces of this solid are included in S.

 

9. Evaluate  where  and S is the portion of the sphere of radius 1 with  and  with the positive orientation.  Note that all three surfaces of this solid are included in S.

 

Surface Integrals Previous Section   Next Section Stokes' Theorem
Line Integrals Previous Chapter  

Calculus III (Assignment Problems) / Surface Integrals / Surface Integrals of Vector Fields    [Notes] [Practice Problems] [Assignment Problems]

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