5.2-solutions - Na(gn2849 5.2 campisi(55842 This print-out...

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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 10.0points Evaluate the definite integral I = integraldisplay 0 - 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 10.0points When f has graph R 1 R 2 a b c express the sum I = integraldisplay c a 2 f ( x ) dx - integraldisplay b a 5 f ( x ) dx in terms of the areas A 1 = area( R 1 ) , A 2 = area( R 2 ) of the respective lighter shaded regions R 1
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