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Unformatted text preview: Miller, Kierste Homework 5 Due: Feb 20 2007, 3:00 am Inst: Gary Berg 1 This printout should have 17 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find the most general function f such that f ( x ) = 5 4 4 x 2 . 1. f ( x ) = 5 x 2 tan 1 x 2 + C 2. f ( x ) = 5 2 + 2 tan 1 x 2 + C 3. f ( x ) = 5 2 x 4 sin 1 x + C 4. f ( x ) = 5 x 4 sin 1 x 2 + C correct 5. f ( x ) = 5 x + 4 sin 1 x 2 + C 6. f ( x ) = 5 + 2 tan 1 x + C Explanation: Since d dx sin 1 x 2 = 1 4 x 2 , we see that f ( x ) = 5 x 4 sin 1 x 2 + C with C an arbitrary constant. keywords: 002 (part 1 of 1) 10 points Find the value of the integral I = Z 5 2 1 9 + ( x 2) 2 dx. 1. I = 3 2. I = 3 3. I = 1 12 correct 4. I = 1 6 5. I = 1 6 6. I = 1 3 Explanation: Set 3 tan u = x 2. Then 9 + ( x 2) 2 = 9 + (3 tan u ) 2 = 9(1 + tan 2 u ) = 9 sec 2 u, while 3 sec 2 udu = dx. Also x = 2 = u = 0 , and x = 5 = u = 4 . In this case I = Z / 4 3 sec 2 u 9 sec 2 u du = 1 3 Z / 4 du. Consequently, I = 1 3 h u i / 4 = 1 12 . keywords: 003 (part 1 of 1) 10 points Evaluate the definite integral I = Z 1 7 1 1 25 x 2 dx. Correct answer: 0 . 159121 . Explanation: Miller, Kierste Homework 5 Due: Feb 20 2007, 3:00 am Inst: Gary Berg 2 Since Z 1 1 x 2 dx = sin 1 x + C , a change of variable x is needed to reduce I to this form. Set u = 5 x . Then du = 5 dx , and x = 0 = u = 0 , while x = 1 7 = u = 5 7 . In this case I = 1 5 Z 5 7 1 1 u 2 du = 1 5 sin 1 u 5 7 . Consequently, I = 1 5 arcsin 5 7 = 0 . 159121 . keywords: 004 (part 1 of 1) 10 points Find the value of the definite integral I = Z 1 2 2 sin 1 x 1 x 2 dx. 1. I = 1 25 2 2. I = 1 36 2 correct 3. I = 1 16 2 4. I = 1 12 2 5. I = 1 9 2 Explanation: Since Z 1 1 x 2 dx = sin 1 x + C , this suggests the substitution u = sin 1 x , for then du = 1 1 x 2 dx, while x = 0 = u = 0 , x = 1 2 = u = 6 ....
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This note was uploaded on 05/08/2008 for the course M 408 L taught by Professor Cepparo during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Cepparo

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