# Math 121 - Chapter 6 Study Guide

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. A curve is given to you along with key points on the curve. Make a table of the midpoints between the left and right endpoints of each interval and the width of each interval. Use the table to find the volume of the solid generated when the region is rotated about the x-axis and the y-axis. Look at problem 6.2.39.
4. Sketch the curve given. Find and simplify the arc length 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.
5. 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 arc length of the curve. Also approximate the area of the surface generated when the curve is rotated about one of the coordinate axes. The closest thing to this in the text is the arc length problem on page 417.
6. Work problem - springs. Look at problems 6.6.4-7.
7. Find the fluid force on the submerged surface. Look at problems 6.7.3-8.
8. Variable work problem. Look at problems 6.6.8-17 with extremely heavy emphasis on 16.

## Notes:

• Show all work and give exact answers except where indicated.
• You should know the weight density of water in the English and metric systems.
• 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.

## Point values for each problem

 # Pts 1 2 3 4 5 6 7 8 Total 16 16 15 15 14 8 8 8 100

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Last updated April 23, 2003 4:11 PM