HW5 - momin(rrm497 – Homework 05 – cheng –(58520 1...

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Unformatted text preview: momin (rrm497) – Homework 05 – cheng – (58520) 1 This print-out should have 13 questions. Multiple-choice 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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HW5 - momin(rrm497 – Homework 05 – cheng –(58520 1...

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