5.2-solutions - Na(gn2849 – 5.2 – campisi –(55842 1...

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Unformatted text preview: Na (gn2849) – 5.2 – campisi – (55842) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the definite integral I = integraldisplay- 2 parenleftBig 2 + radicalbig 4- x 2 parenrightBig dx by interpreting it in terms of known areas. 1. I = 4 π + 4 2. I = 2 π + 4 3. I = π + 4 correct 4. I = π + 2 5. I = 2 π + 2 6. I = 4 π + 2 Explanation: Since the graph of y = 2 + radicalbig 4- x 2 is the upper half of the circle centered at (0 , 2) hav- ing radius r = 2, the value of I is the area of the shaded region in- 2 2 bounded by the graph of y = 2+ radicalbig 4- x 2 , the vertical lines x =- 2, and x = 0 as well as the interval [- 2 , 0]. Consequently, the area is the sum of the area of a quarter-circle of radius r = 2 and a 2 × 2 rectangle, i.e. , I = π + 4 . 002 10.0 points When f has graph R 1 R 2 a b c express the sum I = integraldisplay c a 2 f ( x ) dx- integraldisplay...
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This note was uploaded on 02/11/2011 for the course M 480S taught by Professor Campisi during the Spring '11 term at University of Texas.

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5.2-solutions - Na(gn2849 – 5.2 – campisi –(55842 1...

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