Exercises

Exercises for Lectures #13

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1-8. Evaluate the surface integrals of the first type:

1. where S is the portion of the plane that lies in the first octant.

2. where S is the portion of the plane that lies in the first octant.

3. where S is the portion of the plane that lies in the first octant.

4. where S is the portion of the plane that lies in the first octant.

5. where S is the portion of the sphere that lies in the first octant.

6. where S is the semi-sphere

7. where S is the semi-sphere

8. where S is the semi-sphere

9-10. Evaluate the surface integrals of the second type:

9. where S is the positive side of cube composed by the planes

10. where S is the external side of pyramid composed by the planes

1. Use Stokes' formula to evaluate where and C is the triangle with the vertices (1,0,0), (0,1,0) and (0,0,1) with counter – clockwise rotation.