### Reading Assignments - Math 104 - Calculus II September 1997

Be sure to check back often, because the assignments may change.

#### For September 5

Course Policies

Section 5.1 Areas and Integrals
Section 5.2 The Area Function
Section 5.3 The Fundamental Theorem of Calculus

• To read: All, but you may skip the proof of the Fundamental Theorem of Calculus beginning on page 373.
• Be sure to understand: The major ideas in these sections should be review for you. If you aren't familar with the Area Function, don't despair: we'll talk about it in class.

Email Subject Line: Math 104 9/5 Your Name

1. What does the integral of a function f from x=a to x=b measure?
2. Let f(t)=t and let a=0. What is A_f(2)?
3. Find the area between the x-axis and the graph of y=x^2 + 2 from x=0 to x=2.

#### For September 8

Section 5.4 Approximating Sums
• To read: All. The integral defined as a limit can be tough to get a handle on.
• Be sure to understand: The figures on page 378 and the section Sigma Notation; Partitions

Email Subject Line: Math 104 9/8 Your Name

1. When approximating an integral, which would you expect to be more accurate, L_10 or L_100? Why?
2. Give an example of a partition of the interval [0,3].
3. What is a Riemann sum?

#### For September 10

Section 7.1 The Idea of Approximation
• Be sure to understand: The statement of Theorem 1

Email Subject Line: Math 104 9/10 Your Name

1. Why would we ever want to approximate an integral?
2. Is the function f(x)=x^2 monotone on the interval [0,2]?
3. Let f(x)=x^2. Does Theorem 1 apply to the integral int( f(x), x= -1. . 2) ? Explain.

#### For September 12

Section 7.2 More on Error: Left and Right Sums and the First Derivative
• Be sure to understand: The statement of Theorem 2

Email Subject Line: Math 104 9/12 Your Name

1. Explain in words what K_1 is in Theorem 2.
2. Find a value for K_1 for int( x^2, x= -1. . 2).
3. Use Theorem 2 and your value for K_1 to find an upper bound on the error when using L_100 to approximate int( x^2, x= -1. . 2).

#### For September 15

Section 7.3 Trapezoid Sums, Midpoint Sums, and the Second Derivative
• Be sure to understand: The statement of Theorem 3

Email Subject Line: Math 104 9/15 Your Name

1. Explain in words what K_2 is in Theorem 2.
2. Find a value for K_2 for int( x^2, x= -1. . 2).
3. Use Theorem 3 and your value for K_2 to find an upper bound on the error when using M_100 to approximate int( x^2, x= -1. . 2).

#### For September 17

Section 7.3 Trapezoid Sums, Midpoint Sums, and the Second Derivative (continued)
• Be sure to understand: Example 3

Email Subject Line: Math 104 9/17 Your Name

1. How many subdivisions does the trapezoid method require to approximate int( cos(x^3), x = 0. . 1) with error less than 0.0001?

#### For September 19

No Reading Assignment today because of the project.

#### For September 22

Section 3.8 Inverse Trigonometric Functions and Their Derivatives
This section is from Volume 1, but it is included in Volume 2 starting on page 733.
• To read: All, but you can skip the section on Inverse Trigonometric Functions and the Unit Circle

Email Subject Line: Math 104 9/22 Your Name

1. What is the domain of the function arccos(x)? Why?
2. What is the range of arctan(x)?
3. Find one antiderivative of 1 / (1+x^2).

#### For September 24

Section 6.1 Antiderivatives: The Idea
Section 6.2 Antidifferentiation by Substitution
• Be sure to understand: Examples 3, 5, and 8 from Section 6.2

Email Subject Line: Math 104 9/24 Your Name

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 September 26

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 9/26 Your Name

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 September 29

Exam 1 today. No Reading Assignment.

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