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Unformatted text preview: momin (rrm497) Homework 05 cheng (58520) 1 This printout should have 13 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine the integral I = integraldisplay 4 x (1 2 ln x ) 3 dx. 1. I = 1 2 (1 2 ln x ) 4 + C 2. I = (1 2 ln x ) 4 + C 3. I = (1 2 ln x ) 4 + C 4. I = 1 2 ln x (1 2 ln x ) 2 + C 5. I = 1 2 (1 2 ln x ) 4 + C correct 6. I = ln x (1 2 ln x ) 2 + C 7. I = 1 2 ln x (1 2 ln x ) 2 + C 8. I = ln x (1 2 ln x ) 2 + C Explanation: Set u = 1 2 ln x . Then du = 2 x dx, so I = 2 integraldisplay u 3 du = 1 2 u 4 + C . Consequently, I = 1 2 (1 2 ln x ) 4 + C with C an arbitrary constant. 002 10.0 points Determine the indefinite integral I = integraldisplay 6 x ( x 3) 2 dx . 1. I = ln( x 3) 6 + 18 ( x 3) 2 + C 2. I = 3 ln( x 3) 2 + C 3. I = 6 x 3 + C 4. I = ln( x 3) 6 18 x 3 + C correct 5. I = 18 ( x 3) 2 + C Explanation: Set u = x 3 ; then du = dx , so I = 6 integraldisplay x ( x 3) 2 dx = 6 integraldisplay ( u + 3) u 2 du = 6 integraldisplay du u + 18 integraldisplay u 2 du . But 6 integraldisplay du u = 6 ln  u  + C = ln u 6 + C, while 18 integraldisplay u 2 du = 18 u 1 + C. Consequently, I = ln( x 3) 6 18 x 3 + C . 003 10.0 points Evaluate the definite integral I = integraldisplay 9 1 4 x ( x + 5) dx . 1. I = 8(2 2 6) momin (rrm497) Homework 05 cheng (58520) 2 2. I = 4(2 2 6) 3. I = 4 ln 7 6 4. I = 8 ln 4 3 correct 5. I = 8( 7 6) 6. I = 4( 7 6) 7. I = 4 ln 4 3 8. I = 8 ln 7 6 Explanation: Set u 2 = x . Then 2 u du = dx , while x = 1 = u = 1 x = 9 = u = 3 . In this case, I = 8 integraldisplay 3 1 1 u + 5 du = 8 bracketleftBig ln  u + 5  bracketrightBig 3 1 ....
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 Fall '08
 RAdin
 Calculus

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