Quiz 5 - Math XXXXXXXXXX)Instructions:• The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your scoreon the quiz will be converted to a percentage and posted in your...

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Quiz 5 - 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 29. *********************** 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 5 - Integration Techniques II 1. Chapter 8-4, Problem 6. 2. Chapter 8-4, Problem 8. 3. Evaluate the integral ∫ e2x e2x + 3ex + 2 dx. 4. Evaluate the integral ∫ x+ 4 x2 + 2x+ 5 dx. 5. Evaluate the integral ∫ 4x x3 + x2 + x+ 1 dx. 6. Chapter 8-5, Problem 26. 7. Chapter 8-5, Problem 40. 8. Evaluate the integral ∫ x√ 3− 2x− x2 dx. 9. Chapter 8-6, Problem 8. 10. Evaluate the integral ∫ sec2 x tan2 x+ 3 tanx+ 2 dx. 2 In problems 13-36, evaluate the integrals. (More than one method works for some of the integrals.) rao 18 SN 6? a nfs « 2S In problems 37-42, first complete the square, make the appropriate substitutions, and evaluate the integral wm = wf —s | PROBLEMS Evaluate the integrals. (More than one method works for some of the integrals.) 1 J ion» c JESREREIS x a Ein) ax so J tan ax 6 J cotton ax 0 0 86 Integrals of Trigonometric Functions. Contemporary Calculus 7. J day d 0. J anxreostrn) ax 0 10. J sncrareoin ax snes’ ny ax 12. Fn Gureoson ax 13. J snl anreoan) ax orcas’ Gr) dx 16. J eum on 17. J ed toranin a The definite integrals of various combinations of sine and cosine on the interval [0.27] exhibit a number of interesting patterns. For now these patterns are simply curiousites and a source of additional problems for practice, but the patterns are very important as the foundation for an applied topic. Fourier Series, that you may encounter in more advanced courses. The next three problems ask you to show that the definite integral on [0.251] of sin(mx) multiplied by almost w= In problems 37-42. ET 7 = ! wf a Sm x 85 Trigonometric Substitution Contemporary Calculus Fx) =-5x—1) = + 3(x+2) ~. £700 = 106-17 ~ 60427, and £70 = 300-1 + 182 9x41 Practice 6: Use the partial fraction decomposition of g(x Fo to calculate g(x), £700. and g D0). PROBLEM In problems 1 — 12, decompose the fractions. 7x42 Tx +9 1x +25 LGD TFIG-1 Caos 224 15x +25 6x24 9x15 From XEFHE-1 82 x43 9x24 13x4 15 10. Coax X42" 3x In problems 13 - 30, evaluate the integrals. 3x4 13 2x4 11 so feats ou oy we J alyomea Fax 16. ax 17. Integrate the functions in problems 1-4. 1 Integrate the functions in problems 5 - 8 2045043 224 19x 4 a 0, [BFR exon rents af 3419x424 ax