Math 104 - Calculus II - Reading Assignments
October 1999

Be sure to check back, because this may change during the semester.
(Last modified: Wednesday, October 6, 1999, 9:14 AM )

I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2.

For October 1

Section 9.1 Integration by Parts

  • To read : Through page 497. Be warned that Example 8 is a bit slippery.
  • Be sure to understand : The statement of Theorem 1 and Examples 1, 3, and 6

Email Subject Line : Math 104 10/1 Your Name

Reading Questions :

  1. Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
  2. Pick values for u and dv in the integral int( x * sin(x), x). Use parts to find an antiderivative for x * sin(x).

For October 4

Q & A for Exam 1 today. No Reading Assignment.

For October 6

Section 9.1 Integration by Parts

  • To read : Reread the section
  • Be sure to understand : Example 8

Email Subject Line : Math 104 10/6 Your Name

Reading Questions : Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Why?

  1. int( x*cos(x), x)
  2. int(x*cos(x2),x)

For October 8

Practice Antidifferentiation. No Reading Assignment.

For October 11

Fall Break. No Reading Assignment.

For October 13

Section 8.1 Introduction to Using the Definite Integral
Section 8.2 Finding Volumes by Integration

  • To read : All
  • Be sure to understand : The section from 8.2 on Reassembling Riemann's Loaf and Example 1 from 8.2.

Reading Questions : Since this is the first day after Fall Break, you don't have to send these in.

  1. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis?
  2. Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis?

For October 15

Section 8.2 Finding Volumes by Integration

  • To read : Re-read the section for today
  • Be sure to understand : Example 3

Email Subject Line : Math 104 10/15 Your Name

Reading Questions : Consider the region R bounded by the graphs y=x and y=x2. (Notice R is in the first quadrant). Set up the integral that gives the volume of the solid formed when R is rotated about

  1. the x-axis
  2. the y-axis

For October 18

Section 8.3 Arclength

  • To read : All
  • Be sure to understand : The statement of the Fact at the bottom of page 468, and Example 2.

Email Subject Line : Math 104 10/18 Your Name

Reading Question:

    Use the Fact on page 468 to set up the integral that gives the length of the curve y=x3 from x=1 to x=3.

For October 20

The Big Picture today. No Reading Assignment.

For October 22

Section 10.1 When Is an Integral Improper?

  • To read : All
  • Be sure to understand : Examples 1, 2, and 4. The formal definitions of convergence and divergence on pages 523 and 524.

Email Subject Line : Math 104 10/22 Your Name

Reading Questions :

  1. What are the two ways in which an integral may be improper?
  2. Explain why int( 1/x2, x=1..infty) is improper. Does the integral converge or diverge?
  3. Explain why int( 1/x2, x=0..1) is improper. Does the integral converge or diverge?

For October 25

Work on Project 2 today. No Reading Assignment.

For October 27

Section 10.2 Detecting Convergence, Estimating Limits

  • To read : All
  • Be sure to understand : Example 2 and the statement of Theorem 1

Email Subject Line : Math 104 10/27 Your Name

Reading Questions :

  1. If 0 < f(x) < g(x) and int( g(x), x=1. . infty) converges, will int(f(x), x=1. .infty) converge or diverge? Why?
  2. There are two types of errors that arise in Example 2 for approximating int( 1/(x5 +1), x=1..infty). What are the two types?

For October 29

Section 10.2 Detecting Convergence, Estimating Limits

  • To read : Reread the section.
  • Be sure to understand : The statement of Theorem 2.

Email Subject Line : Math 104 10/29 Your Name

Reading Questions : Suppose that 0 < f(x) < g(x).

  1. If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
  2. If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?


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Last modified: Wednesday, October 6, 1999, 9:14 AM