Mt 217 Accelerated Calculus - Fall 2003

Assignment 9: More on Antiderivatives and Definite Integrals

November 3, 2003

Purpose

During class this week, we will continue to work with antiderivatives and definite integrals.

A Midsemester Reflection -- DUE by noon on Wednesday, November 5

As it is just past the middle of the semester, it is good to take a look at how far we have come in this course -- and how much farther we need to go. You have each received some mid-semester feedback from me, and I would appreciate hearing your feedback to me. Please review the course objectives for this course, and send me your reflective responses to the following questions by email by noon on Wednesday, November 5.

1. What is your sense of the progress you are making in meeting the course objectives and content goals?
2. What aspects of the course do you feel are working well for you? What do you feel is working poorly?
3. Identify two or three things that you can do which would help you to meet the objectives and content goals of this course.
4. In what ways have your experiences in this course helped you to understand Franciscan values more deeply?
5. In what way(s) could Sister Barbara help you to do the things you identify in item 3?

Homework Assignments

You need to do enough problems to develop fluency with evaluating antiderivatives and definite integrals. In class discussion this week, we will be working on some of the higher-numbered exercises in Sections 5.5, 5.6, and 5.7. These require computation skill, a conceptual understanding of integration, and some cleverness.

• Work lots of the odd-numbered problems in Section 5.5. Bring some of these to class for discussion.
• Work lots of the odd-numbered problems in Section 5.6. Bring some of these to class for discussion.
• Work lots of the odd-numbered problems in Section 5.7. Bring some of these to class for discussion.

Work on problems from the sheet of 75 antiderivatives.

• Write up the solution to 15 of there problems to turn in on Thursday -- this Thursday, next Thursday, and the following Thursday. There is just no substitute for practice -- practice -- practice.

Opportunities for Extra Credit

• The Sight Distance Problem -- DUE: November 6

The Sight Distance Problem is an important problem in the design of highways. To solve this problem, you need to use properties of parabolas beyond those that are discussed in the Student Resource Book for the Highway Slope Design problem. If you choose to do this problem, write up your solution as a formal memo to the civil engineer in the Department of Transportation who contracted you to solve the problem. The grading rubric for this problem will be the same as that for the Highway Slope Design project.

• Calculating Antiderivatives -- the sheet of 75 problems

For each 15 of the problems on the sheet of antiderivative problems that you solve correctly, write up, and turn in, you may earn 5 points of extra credit. I will keep track of your extra credit points for this assignment, and use this in computing your final grade for this course. (Since there are 75 problems on this sheet, you may earn up to 25 extra credit points in this way.) You may turn in sets of these problems on Thursdays -- November 6, 13, 20, and Wednesday Noverber 26.

You may work together on these problems, and you may get Maple or a calculator with a CAS to help you solve these problems. You must write up your solutions individually. For each problem that you solve, your write-up must show the following:

• Show the solution. Write out the problem and the solution you calculate by hand.

• Write one or two sentences in which you

  • name the method you used, and
  • how you recognized that this method would work.