## Math 121 - Chapter 6 Exam

1. Setup the integral necessary to find the arc length of a parametric curve. Use your calculator to approximate the integral to three decimal places.
2. Find the fluid force on the submerged surface. Look at problems 6.7.3-8.
3. Sketch the region enclosed by the curves and find its area. Two parts. Look at problems 6.1.7-14.
4. Sketch the region described in the x-y plane and then find the volume when the region is rotated about one of the axes. Four parts. Identify the method used to find the volume. You may use the disk method, washer method, or cylindrical shell method, but you must use each method at least once. Look at problems 6.2.5-20 and 6.3.5-14.
5. Find the exact arc length of the curve over the given interval. Two parts. Look at problems 6.4.3-8.
6. Find the surface area of revolution when the curve is rotated about the indicated axes. Two parts. Look at problems 6.5.1-8.
7. Work problem - springs. Look at problems 6.6.4-7.
8. Variable work problem. Look at problems 6.6.8-17.
9. Approximate the area between two curves using the midpoints of the intervals. Look at problem 6.2.39 except apply it to the area of the region instead of the volume of revolution.

### Notes:

• Some of the problems are directly from the textbook.
• Show all work and give exact answers except where indicated.
• There are some problems (indicated on the test) where you are to set up the integral and then use the TI89 or Derive to find the exact answers. There are other problems where you will need to use the numerical integration techniques of your calculator to find the answer.
 # 1 2 3 4 5 6 7 8 9 Total Pts 6 8 12 24 12 12 8 8 10 100