Math 104 - Calculus II
Reading Assignments - September 2004

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

For Friday September 3

Section 5.1 Areas and Integrals
Section 5.2 The Area Function
Section 5.3 The Fundamental Theorem of Calculus
Section 3.4 Inverse Functions and Their Derivatives (at the back of the book)

To read : Sections 5.1, 5.2, and 5.3 should be review, so you can skim these to remind yourself of the Fundamental Theorem of Calculus.
You can skim the beginning of Section 3.4, but read the section Working with inverse trigonometric functions beginning on page S-8 carefully.

Be sure to understand : The statements of both forms of the Fundamental Theorem of Calculus. The derivatives of the inverse trig functions.

Reading Questions :

1. What is the domain of the function arccos(x)? Why?
2. Why do you think we studying the inverse trig functions now?
3. Find one antiderivative of 1 / (1+x²).

For Wednesday September 8

Section 5.4 Finding Antiderivatives; The Method of Substitution

To read : All

Be sure to understand : Examples 6, 7, 10, and 13

Reading Questions :

1. Explain the difference between a definite integral and an indefinite integral.
2. What are the three steps in the process of substitution?
3. Substitution attempts to undo one of the techniques of differentiation. Which one is it?

For Friday September 10

Section 5.6 Approximating Sums; The Integral as a Limit

To read : All

Be sure to understand : Examples 2 and 3

Reading Questions :

1. When approximating an integral, which would you expect to be more accurate, L₁₀ or L₁₀₀? Why?
2. Give an example of a partition of the interval [0,3].
3. Explain the idea of a Riemann sum in your own words.

For Monday September 13

Section 6.1 Approximating Integrals Numerically

To read : All

Be sure to understand : The statements of Theorem 1 and Theorem 2

Reading Questions :

1. Why would we ever want to approximate an integral?
2. Let f(x)=x² and I=int( f(x), x= -1. . 2). Does Theorem 1 apply to I? Explain.
3. Let f(x)=x² and I=int( f(x), x= -1. . 2). Does Theorem 2 apply to I? Explain.

For Wednesday September 15

Section 6.2 Error Bounds for Approximating Sums

To read : All

Be sure to understand : The statement of Theorem 3 and Example 6.

Reading Questions :

1. Explain in words what K₁ is in Theorem 3.
2. Explain in words what K₂ is in Theorem 3.
3. Let I=int( x³, x= -1. . 3). Is 2 a valid value for K₁ in Theorem 3? Explain.

For Friday September 17

Section 6.2 Error Bounds for Approximating Sums

To read : Reread the section, but no Reading Questions for today.

For Monday September 20

Section 7.1 Measurement and the Definite Integral; Arc Length

To read : All

Be sure to understand : The Fact on page 416, Example 5, the Fact on page 419, and Example 8.

Reading Questions :
Let f(x)=sin(x)+10 and g(x)=2x-5.

1. Set up the integral that determines the area of the region bounded by y=f(x) and y=g(x) between x=-1 and x=3.
2. Set up the integral that gives the length of the curve y=g(x) from x=-1 to x=3.

For Wednesday September 22

For Friday September 24

Section 7.2 Finding Volumes by Integration

To read : All

Be sure to understand : The section Solids of revolution

Reading Questions :

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 Monday September 27

Section 7.2 Finding Volumes by Integration

To read : Reread the section, but no Reading Questions for today.

For Wednesday September 29