Fall 1999, Math 101

CHAPTER 5

Be sure to check back often, because assignments may change!

Due Friday 11/19 at 9am

Section 5.1 Areas and Integrals

• Be sure to understand: The definition of the integral on page 342; Example 2; the section Properties of the Integral beginning on page 345

Section 5.2 The Area Function

• Be sure to understand: The definition of the area function on page 357; Examples 1 and 2

E-mail Subject Line: Math 101 Your Name 11/19

1. What does the integral of a function f from x=a to x=b measure?
2. Is the integral of f(x)=5x from x= -1 to x=3 positive or negative? Why?
3. Let f be any function. What does the area function Af(x) measure?
4. Let f(t)=t and let a=0. What is Af(1)?

Reminder:

• PS 10 is due by Friday at 4pm.
• You should be well on the way to producing a draft of a letter for Liz Parker. Have a friend read it without telling them the assignment--it ought to stand on its own.
• Midterm 3 is the Thursday after Thanksgiving break. Start studying now. Make sure you've done every assigned problem!

Due Monday 11/22 at 9am

Section 5.3: The Fundamental Theorem of Calculus

• To read: All, although you may skim the proof of the FTC beginning on page 373-we'll prove it a different way in class.
• Be sure to understand: The statement of both the first and second forms of the FTC; Example 3

E-mail Subject Line: Math 101 Your Name 11/22

1. Find the area between the x-axis and the graph of f(x)=x3+4 from x=0 to x=3.
2. Does every continuous function have an antiderivative? Why or why not?
3. What is the difference between a definite integral and an indefinite integral?

Reminder:

• Project 2 is due Monday at 4pm.
• In your spare time (hah hah), continue studying for the midterm, so you don't have to over break.

Due Monday 11/29 at 9am

Reminder:

• If you're caught up and have already started studying for the exam, take the break off! If youv'e gotten behind, use Thanksgiving break as a marvelous opportunity to catch up!

Due Wednesday 12/1 at 9am

Section 5.3 The Fundamental Theorem of Calculus

• Be sure to understand: Make sure you really understand both statements of the FTC.

E-mail Subject Line: Math 101 Your Name 12/1

1. If f(x)=3x-5 and a=2, where is Af increasing? decreasing? Why?

Reminder:

• PS 11 will not be turned in, due to the exam, but you should still, of course, do it and bring questions to class Wednesday.
• Keep on studying. I'll probably have a review session Wednesday night at 9pm again, but keep an ear out for announcements in class.

Due Friday 12/3 at 9am

No reading, due to the exam!

Reminder:

• While I'm not collecting PS 11, you should have it done by Friday.
• The final is self-scheduled. Start thinking about when you'd like to take it, and planning when and how you're going to study for it.

Due Monday 12/6 at 9am

Section 5.4 Approximating Sums: The Integral as a Limit

• To read: Through page 381
• Be sure to understand: The figures on page 381

E-mail Subject Line: Math 101 Your Name 12/6

Let f(x)=x2 and let I represent the integral of f from x=0 to x=3.
1. Estimate I by finding L3, the left sum with 3 equal subintervals.
2. Estimate I by finding R3, the right sum with 3 equal subintervals.

DueWednesday 12/8 at 9am

Section 5.4 Approximating Sums: The Integral as a Limit

Reminder:

• Bring questions on PS 12 to class Wednesday.
• The final will be self-scheduled.
• Be reviewing for the final, of course. Redo as many problems from the entire semester as possible.

Due Friday 12/10 at 9am

Section 5.4 Approximating Sums: The Integral as a Limit

• Be sure to understand: The definition of a Riemann sum and the definition of the integral as a limit on page 383.

E-mail Subject Line: Math 101 Your Name 12/10

Let f(x)=x2 and let I represent the integral of f from x=0 to x=3.
1. Will Ln underestimate or overestimate I? Why?
2. Will Rn underestimate or overestimate I? Why?

Reminder:

• PS 12 is due Friday at 4pm.
• Take notes on the main points of every section, and look for connections between ideas.

Due Monday 12/13 at 9am

Reminder:

• Study a lot! In addition to what I've already suggested, redo all the exam problems and look over old study guides.

Here ends the semester!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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