### Math 104 - Calculus II - Reading Assignments February 1999

Be sure to check back, because this may change during the semester.

All numbers indicate sections from Ostebee/Zorn, Vol 2.

### For February 3

Course Policies

Section 5.1 Areas and Integrals
Section 5.2 The Area Function
Section 5.3 The Fundamental Theorem of Calculus
Section 5.4 Approximating Sums

• To read : All, but you may skip the proof of the Fundamental Theorem of Calculus beginning on page 373. The major ideas in these sections should be review for you.
• Be sure to understand : The figures on page 378 and the section Sigma Notation; Partitions begining on page 380

Email Subject Line : Math 104 2/3 Your Name

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. What is a Riemann sum?

### For February 5

Section 7.1 The Idea of Approximation

• Be sure to understand : The statement of Theorem 1

Email Subject Line : Math 104 2/5 Your Name

1. Why would we ever want to approximate an integral?
2. Give an example of a function that is monotone on the interval [0,2].
3. Let f(x)=x2. Does Theorem 1 apply to the integral int( f(x), x= -1. . 2) ? Explain.

### For February 8

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 2/8 Your Name

1. Explain in words what K1 is in Theorem 2.
2. Find a value for K1 for int( x2, x= -1. . 2).
3. Use Theorem 2 and your value for K1 to find an upper bound on the error when using L100 to approximate int( x2, x= -1. . 2).

### For February 10

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 2/10 Your Name

1. Explain in words what K2 is in Theorem 2.
2. Find a value for K2 for int( x2, x= -1. . 2).
3. Use Theorem 3 and your value for K2 to find an upper bound on the error when using M100 to approximate int( x2, x= -1. . 2).

### For February 12

The Big Picture

• Be sure to understand : Example 3

Email Subject Line : Math 104 2/12 Your Name

How many subdivisions does the trapezoid method require to approximate int( cos(x3), x = 0. . 1) with error less than 0.0001?

### For February 15

Work on Group Project 1. No Reading Assignment.

### For February 17

Section 3.8 Inverse Trigonometric Functions and Their Derivatives

• To read : All, but you can skip the section on Inverse Trigonometric Functions and the Unit Circle
• Be sure to understand :

Email Subject Line : Math 104 2/17 Your Name

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

### For February 19

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 2/19 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 February 22

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 2/22 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 February 24

Section 9.1 Integration by Parts

• Be sure to understand : Example 8

Email Subject Line : Math 104 2/24 Your Name

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 February 26

Exam 1 today. No Reading Assignment.

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