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Chapter 14: Q. 58 (page 1134)
Give an example of a vector field defined on a simply connected regionR 鈯� whose boundary is smooth or piecewise smooth, that is not a conservative field, but whose integral over the unit disk does have the property that
Your example shows that the converse of Exercise 57 fails.
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Find the areas of the given surfaces in Exercises 21鈥�26.
S is the lower branch of the hyperboloid of two sheets that lies below the annulus determined by in the xy plane.
Find the work done by the vector field
in moving an object around the periphery of the rectangle with vertices , and , starting and ending at .
Problem Zero: Read the section and make your own summary of the material.
What does it mean to say that a vector field is conservative?
What is the difference between the graphs of
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