EXAM 3
Math 142-503
April 19, 2000

Name
SSN

1. Integrate each of the following.
   1. (6 pts)
   2. (6 pts)
   3. (6 pts)
   4. (6 pts)

2. (8 pts) Suppose the rate of production at which copper is being extracted from a mine during the early and intermediate stages of the life of the mine is given by (in tons per year). Find the amount of copper extracted during the first two years.

3. (10 pts) An object travels with a velocity function given by . Divide the interval [1,3] into five intervals and find the left and right Riemann Sums. On the axes below draw the corresponding pictures.
   
   

   

4. (10 pts) Use Riemann sums with n = 10 to estimate the value of

   

   and then use n=100 to improve your estimate.

5. Find each of the following definite intervals.
   1. (6 pts)
   2. (6 pts)

6. (8 pts) Find the average value of the function on the interval [1,3].
7. (10 pts) Find the absolute maximum and minimum for on [-1,3].

8. (8 pts) Find the area between the curves and g(x)=x on the interval [-8,1].
9. (8 pts) A closed rectangular box with a volume of 324 cubic inches is to be made with a square base. If the material for the bottom costs twice as much per square inch as the material for the sides and top, find the dimensions of the box that minimize the cost of materials.

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