Homework 8 - Rehman (aar638) HW08 sachse (56620) 1 This...

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Unformatted text preview: Rehman (aar638) HW08 sachse (56620) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Evaluate the integral I = integraldisplay 2 1 16- x 2 dx . 1. I = 1 6 2. I = 1 4 3. I = 1 3 4. I = 1 4 5. I = 1 6 correct 6. I = 1 3 Explanation: Set x = 4 sin u ; then dx = 4 cos u du and 16- x 2 = 16(1- sin 2 u ) = 8 cos 2 u , while x = 0 = u = 0 , x = 2 = u = 6 . In this case I = integraldisplay / 6 cos u cos u du = integraldisplay / 6 du . Consequently I = 1 6 . 002 10.0 points Evaluate the integral I = integraldisplay 1 x 2 (2- x 2 ) 3 / 2 dx . 1. I = 2 parenleftBig 3- 3 parenrightBig 2. I = 2 parenleftBig 3 + 3 parenrightBig 3. I = 1- 4 correct 4. I = 2 parenleftBig 2 + 3 parenrightBig 5. I = 2- 4 6. I = 1 + 4 Explanation: Let x = 2 sin . Then dx = 2 cos d , 2- x 2 = 2 cos 2 , while x = 0 = = 0 , x = 1 = = 4 . In this case, I = integraldisplay / 4 2 2 sin 2 cos 2 2 cos 3 d = integraldisplay / 4 sin 2 cos 2 d = integraldisplay / 4 tan 2 d . Now tan 2 = sec 2 - 1 , d d tan = sec 2 , and so I = integraldisplay / 4 (sec 2 - 1) d = bracketleftBig tan - bracketrightBig / 4 . Consequently, I = 1- 4 . Rehman (aar638) HW08 sachse (56620) 2 003 10.0 points Evaluate the integral I = integraldisplay 1 3 ( x 2 + 3) 3 / 2 dx . 1. I = 3 2. I = 3 2 3. I = 1 4. I = 3 4 5. I = 1 2 correct Explanation: Set x = 3tan u. Then dx = 3sec 2 u du , while x = 0 = u = 0 , x = 1 = u = 6 . On the other hand, ( x 2 + 3) 3 / 2 = ( 3(tan 2 u + 1) ) 3 / 2 = 3 3 sec 3 u . Thus I = 3 integraldisplay / 6 3 sec 2 u 3 3sec 3 u du = integraldisplay / 6 cos u du = bracketleftBig sin u bracketrightBig / 6 . Consequently I = 1 2 . keywords: 004 10.0 points Evaluate the definite integral I = integraldisplay 2 2 4 x 2 x 2- 1 dx . 1. I = 4( 3- 2) 2. I = 2( 3 + 2) 3. I = 3 + 2 4. I = 3- 2 5. I = 2( 3- 2) correct 6. I = 4( 3 + 2) Explanation: Set x = sec u . Then dx = sec u tan u du , x 2- 1 = tan 2 u , while x = 2 = u = 4 , x = 2 = u = 3 . In this case, I = 4 integraldisplay / 3 / 4 sec u tan u sec 2 u tan u du = integraldisplay / 3 / 4 4 cos u du = 4 bracketleftBig sin u bracketrightBig / 3 / 4 . Consequently, I = 2( 3- 2 ) . 005 10.0 points Rehman (aar638) HW08 sachse (56620) 3 Which one of the following functions is an antiderivative of f when f ( x ) = 1 x 2- 6 x + 10 ?...
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This note was uploaded on 02/01/2011 for the course MATH 408L taught by Professor Gogolev during the Fall '09 term at University of Texas at Austin.

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Homework 8 - Rehman (aar638) HW08 sachse (56620) 1 This...

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