Math 120 Spring 98

Quiz 6  Basic Calculus 2

Name:

Date:  Friday March 27, 1998
Time Begun:  Ron Buckmire

Time Ended:

Topic covered: Improper Integrals

The idea behind this quiz is to give you more practice evaluating improper integrals and to review the inverse trigonometric function arctan(x).

Instructions:

1. Once you open the quiz, you have 60 minutes to complete it.

2. You may use the book or any of your class notes, and you may use a calculator. You must work alone.

3. If you use your own paper, please staple it to the quiz before coming to class. If you don’t have a stapler, buy one.

4. After completing the quiz, sign the pledge below stating on your honor that you have adhered to these rules.

5. Relax and enjoy...

6. This quiz is due on Monday, March 30, in class. NO LATE QUIZZES WILL BE ACCEPTED.

Pledge: I, , pledge my honor as a human being and Occidental student, that I have followed all the rules above to the letter and in spirit.

Math 120 Spring 1998 Quiz 6

SHOW ALL YOUR WORK

1. (2 points) Compute the derivative of f(x) = arctan(2x). (The inverse of the trigonometric function tan(x) is known as arctan(x).)

2. (4 points) Your answer above should assist you in �nding the antiderivative of \frac{4}{1 + (2x)^{2}}.

That is, evaluate the following integral.

∫ \frac{4}{1 + 4x^{2}} dx =

3. (4 points) Use your answer from (2) to determine whether the following improper integral converges to a �nite value or not. If it converges, compute its value exactly.

∫_{0}^{∞} \frac{4}{1 + 4x^{2}} dx =