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Unformatted text preview: moraboellstorff (erm823) – 5.2 – Arledge – (55875) 1 This printout should have 6 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the definite integral I = integraldisplay 4 parenleftBig 2 + radicalbig 16 x 2 parenrightBig dx by interpreting it in terms of known areas. 1. I = 4 π + 4 2. I = 8 π + 4 3. I = 8 π + 8 4. I = 4 π + 8 correct 5. I = 16 π + 8 6. I = 16 π + 4 Explanation: Since the graph of y = 2 + radicalbig 16 x 2 is the upper half of the circle centered at (0 , 2) having radius r = 4, the value of I is the area of the shaded region in 4 2 bounded by the graph of y = 2 + radicalbig 16 x 2 , the vertical lines x = 4, and x = 0 as well as the interval [ 4 , 0]. Consequently, the area is the sum of the area of a quartercircle of radius r = 4 and a 4 × 2 rectangle, i.e. , I = 4 π + 8 ....
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This note was uploaded on 02/02/2011 for the course M 408 S taught by Professor Alredge during the Fall '10 term at University of Texas.
 Fall '10
 Alredge

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