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067Exam4soln - EXAM 4 Section December 7 2006 NAME Make...

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EXAM 4 Section December 7, 2006 NAME: Make sure to read the question carefully and answer the question that is asked. Show ALL relevant work so that partial credit may be given and indicate where the solution is. Lack of sufficient work may result in a loss of credit, even if a correct answer is given. Good luck!! “On my honor, as a University of Colorado at Boulder student, I have neither given nor received unautho- rized assistance on this work.” YOUR SIGNATURE: 1. True or False (1 point each) Determine whether each of the following statements is True of False and circle the appropriate response. Note that no work is required and no partial credit is possible. (a) x 5 - 4 x + 9 is an antiderivative of 5 x 4 - 4. True False Solution: True. integraldisplay 5 x 4 - 4 dx = 5( x 5 5 ) - 4 x + C = x 5 - 4 x + C . When C = 9 x 5 - 4 x + 9 is an antiderivative of 5 x 4 - 4. Alternatively, the derivative of x 5 - 4 x + 9 is 5 x 4 - 4 and hence x 5 - 4 x + 9 is an antiderivative of 5 x 4 - 4. (b) The value of integraldisplay 2 0 (1 - x ) dx is equal to the area of the region under the graph of f ( x ) = x - 1 on the interval [0 , 2]. True False Solution: False. integraldisplay 2 0 (1 - x ) dx = 0 while the area of between the graph of f ( x ) = x - 1 and the x - axis on the interval [0 , 2] is equal to 1.
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