Friday, February 1,      Review

Practice test.  The real test is Monday, February 4, 2008 

                                                       2
1.  Find the volume when the portion of the curve y = x   + x - 6 

which lies below the x-axis, and to the right of the y-axis 

is rotated about the y axis.  

















2.  Find the volume when the portion of the curve

                    2
               y = x   + x - 6 

which lies below the x-axis, is rotated about the x axis.


















3.  Find the y coordinate of the Centroid of the area under y = Tan[x] from

x=0 to x = Pi/4.

















4.  Find the length of the curve  r(t) = {1-Cos[t], Sin[t]}

from t = 0 to t = Pi. 



















5.  A spring requires 8 pounds to stretch it 3 inches.

(a)  How much will a force of 82.5 pounds stretch it?

(b)  How much work is required to stretch it 18 inches?




















6.  Find the Centroid of the following figure.

                   10
            ---------------
            |             |                
            |             |                
          9 |             |8
            |             |     10           
            |             |______________  
            |    8                       | 
            ----------                   | 
                      |                  | 7 
                     6|                  | 
                      |                  | 
                      --------------------
                              12







7.  A car weights 5000 pounds.  It is on a bridge

500 feet from end A and 900 feet from end B.

(a) How much of the weight of the car supported by end A.  

(b) How much of the weight of the car supported by end B.  






















8.  A plane passes 5 inches from the center of a sphere of

radius 6.  What is the volume of the slice.


                ... ...
   _________.______|_____.___________________
          .        |       .
         .         |        .
         .         |        .
         .---------+--------.
         .         |        .
          .        |       .             
           .       |      .       2     2
            .      |     .       x   + y   = 36
              ` ...|... ' 

























9.  How much work is done pumping the water from a cone

out over the top of the cone.
    
        <------20----->
        \            / /|\
         \          /   |
          \_______ /    |
           \      //|\  30 ft 
            \    /  |   |
             \  /  8 ft |
              \/   \|/ \|/




















10.  Find the surface area of the surface of the

volume formed when one arch of the curve y = Sin[x]

is rotated about the x-axis.