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Quiz 4 - Math 141 (7380) Instructions: • The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. • This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. • You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. • Please write neatly. Illegible answers will be assumed to be incorrect. • Please remember to show ALL of your work on every problem. Read the basic rules for showing work below BEFORE you start working on the quiz: 1. Each step should show the complete expression or equation rather than a piece of it. 2. Each new step should follow logically from the previous step, following rules of algebra. 3. Each new step should be beneath the previous step. 4. The equal sign, =, should only connect equal numbers or expressions. • This quiz is due at 11:59 PM (Eastern Time) on Tuesday, November 22. *********************** At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name: Date: 1 Quiz 4 - Integration Techniques I 1. Chapter 8-1, Problem 2. 2. Chapter 8-1, Problem 8. 3. Chapter 8-1, Problem 18. 4. Chapter 8-1, Problem 30. 5. Chapter 8-2, Problem 44. 6. Chapter 8-2, Problem 50. 7. Evaluate the integral ∫ e2t cos(3t) dt. 8. Chapter 8-3, Problem 36. 9. Evaluate the integral ∫ √3 1 arctan (1 x ) dx. 10. Using integration by parts, calculate ∫ √π √ π/2 x3 cos(x2) dx. 2 x-axis for x 2 1 and the graph of 10) = S52 (Fig. 12) is revolved about the x-axis. (@ The volume obtained when the area between the positive x-axis (x20) and the graph of 1 0 = 777 (Fig. 13a) i revolved about the x-axis. (b) The volume obtained when the area between the positive x-axis (x20) and the graph of 1 0 = 77,7 (Fig. 130) is revolved about the y-axis. (Use the method of “tubes from section 5.5) 32. (3) The volume obtained when the area between the positive x-axis (x20) and the graph of 1 x)= is revolved about the x-axis. PY kX) re] xeln(x) Contemporary Calculus incon nnd 27 wos o . : Example 30) showed hat J ds. grew abivarily large a C grew abil lrg, so fn 1 amount of paint would cover the area bounded between the x-axis and the graph of f(x) = Ix for x > 1 (Fig. 113). Show that the volume obiained when the area in Fig. 11 is revolved abou the 2] J wean a ow Jeenta In problems 43 - 48, complete the square in the denominator, make the appropriate substitution, and integrate. ofr wf —w is Tram 1 3 a6 J —a a. J—=— S20 10 Fr10:+29 dx 4. In problems 49 — 54, evaluate the first integral as a sum of two integrals. 20411 ares axa 448 50 Jp a ft de Iris ax = . er of ae fw Zoersto MTT Taino © orto Jw Ere Imire y ax=9 J dr ax. wernow fz ox isdivergem 1x 1* bythe P-Test = 12.1), 50 we cam conclude that J 2 an is ivergent. s In 1-21, use the definition of an improper integral o evaluate the given integral. Ike Jt yi Lwin? J Lex , xine) Contempo