# Math 121 - Chapter 6 Study Guide

- 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.
- 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.
- 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.
- 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.
- 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.
- Work problem - springs. Look at problems 6.6.4-7.
- Find the fluid force on the submerged surface. Look at problems 6.7.3-8.
- 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

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Total |

Pts |
16 |
16 |
15 |
15 |
14 |
8 |
8 |
8 |
100 |

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Last updated
April 23, 2003 4:11 PM