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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

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