## Math 121 - Chapter 6 Exam

1. Sketch the region enclosed by two curves. Find the area of the region. Find the volume when the region is rotated about one of the coordinate axes. Look at problems 6.1.7-14, 6.2.5-20, and 6.3.5-14.
2. Sketch the region enclosed by two curves. Find the area of the region by setting up an appropriate definite integral and then using the TI89, TI92, or Derive to evaluate the integral. Find the volume when the region is rotated about one of the coordinate axes by setting up an appropriate definite integral and then using the TI89, TI92, or Derive to evaluate the integral. Look at problems 6.1.7-14, 6.2.5-20, and 6.3.5-14.
3. Sketch the curve given. Find and simplify the arclength parameter sqrt [ (dx/dt)2 + (dy/dt)2 ] where dt could be dt, dx, or dy. Then use the results to find the length of the curve and the also to find the surface area of the surface generated when the curve is rotated about one of the coordinate axes. In each case, use a computer algebra system (TI89, TI92, or Derive) to evaluate the integrals. Look at problems 6.4.3-8 and 6.5.1-8.
4. A curve is given to you along with key points on the curve. Find the distance between consecutive points using Pythagorean's theorem and use the distances to approximate the arclength of the curve. Also approximate the area of the surface generated when the curve is rotated about one of the coordinate axes.
5. Work problem - springs. Look at problems 6.6.4-7.
6. Find the fluid force on the submerged surface. Look at problems 6.7.3-8.
7. Variable work problem. Look at problems 6.6.8-17 with heavy emphasis on 16.
8. Find the area between two curves by dividing the region into intervals, measuring the distance between the curves, finding areas of rectangles, and summing.

### 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 Total Pts 16 14 18 14 8 8 8 14 100