Problem Set 7—Integration Miscellany

Purpose

This problem set reinforces your ability to use the methods of integration we have studied or used so far in this course.

Background

This problem set focuses on the methods of integration discussed in sections 8.1 through 8.5 of our textbook. We discussed this material in lectures between February 5 and February 24.

This problem set also draws on integration formulas for transcendental functions, developed in chapter 7 of the textbook and discussed in class between January 27 and February 3.

Finally, this problem set briefly exercises material on improper integrals from section 8.8 of the textbook. I expect to discuss this material in class on February 26.

Activity

Solve each of the following problems:

Problem 1

Evaluate

Problem 2

Evaluate

Problem 3

Exercise 12 in section 8.4 of our textbook (integrate √(y²-25) / (y³)).

Problem 4

Evaluate

Problem 5

Exercise 4 in section 8.8 of the textbook (evaluate the integral from 0 to 4 of dx / √(4-x)).

Follow-Up

I will grade this exercise in a face-to-face meeting with you. During this meeting I will look at your solution, ask you any questions I have about it, answer questions you have, etc. Please bring a written solution to the exercise to your meeting, as reading through it will help me know what to focus on in the rest of the meeting.

Sign up for a meeting via Google calendar. If you worked in a group on this exercise, the whole group should schedule a single meeting with me. Please make the meeting 15 minutes long, and schedule it to finish before the end of the “Grade By” date above.

My basic expectation in grading this exercise is that your solution will show that you understand how to solve each problem, although there may be arithmetic or copying mistakes, inefficient solution methods, incorrect or irrelevant statements incidental to the solution, or similar minor mistakes. If you understand how to solve all the problems and have no minor errors, I will consider the solution to be in between “what I expect” and “surprisingly beyond expectations.” I will consider solutions to be 3/4, 1/2, 1/4, or none of what I expect according to what (rough) fraction of the problems your solution shows understanding of, although I will raise grades slightly if it is clear by the end of your grading meeting that you have come to understand things you didn’t understand when you arrived at the meeting.