CH- Math141_Quiz 5 (2)

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University of Maryland Global Campus (UMGC) *

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141

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Mathematics

Date

Jan 9, 2024

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docx

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11

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NAME: SCORE: Take-Home Quiz # 5 (Sections 8.4 – 8.6) Math 141/7382, Due 11:59PM, Tuesday, November 28, 2023 I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 5 problems. This quiz is open book and open notes . This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Tuesday, 28 November 2023 . Complete the remaining problems to the best of your ability. Even if you cannot come to a final solution, you should show what you do know so that you have the opportunity for partial credit. Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Unit Quizzes module. If you have any questions, please contact me by e-mail at robert.m.smith@faculty.umgc.edu 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: Elsabet Bekele Date:11/28/2023 QUIZ # 5 Problems (Please extend sufficient space if you work on the docx version) 1. Find the partial fraction decomposition for the rational function x 2 x + 5 x 3 + x
2. Use the partial fraction decomposition of the function to evaluate the integral x + 5 x ( x 1 ) 2 dx Solving using a formula is not acceptable. 3. Evaluate each of the following integrals, using a trigonometric substitution . Do not forget the back substitution. Solving using other methods is not acceptable. (a) (b) (c) 4. First complete the square, make the appropriate substitutions, and then evaluate the integral: 5. Evaluate each of the following integrals, using the given substitution or identity. Solutions using other methods are not acceptable. (a) (substitution ) (b) (substitution ) (c) ( ) (d) ( )
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