Test 3 Review
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PART I (56 points, 8 problems each worth 7 points) Multiple choice
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1. Evaluate the triple integral.

   WW. 12.5, 1, 2, 3


2. Triple integral in spherical coordinates

   WW.12.7, 7,8 


3. Calculate the line integral of the first type.

   WW.13.2, 2


4. Triple integral in cylindrical coordinates.

   WW. 12.6, 10 


5. Only one of the following vector fields is conservative.
    Determine which one it is.
 
   WW. 13.3, 1 (You do not need to calculate f(x,y))


6. Which of the following represents the double integral ... in polar coordinates?

   WW. 12.3, 14


7. EValuate a double integral over a domain bounded by ...

   WW. 12.2, 16, 17


8. Calculate the line integral of the 2nd type (circulation, work)  

   WebW.13.2, 6, 8 
   WebW.13.3, 8







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PART II (44 points) Free response
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1. Find the volume.

  WW. 12.6, 6, 7 
  WW. 12.7, 11



2. An object moves along a curve from a point A to a point B through a force field F.
   Find the work done on the object by F.  

   WW. 13.2, 4, 5


3. Evaluate an integral by switching the order of integration. 

 a) Draw an accurate sketch of the region of integration in the xy plane and shade it in.

 b) Evaluate the integral by switching the order of integration. Note that the integral is impossible to do in its current form, but will be possible once the ordering is switched. Give an exact answer; no approximations.

  WW.12.2, 10, 11