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HW07-solutions

# HW07-solutions - wei(jw35975 HW07 kalahurka(55230 1 10 This...

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wei (jw35975) – HW07 – kalahurka – (55230) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points If the points (0 , 5) , ( 1 2 , 3) , (1 , 8) , ( 3 2 , 2) , (2 , 2) lie on the graph of a continuous function y = f ( x ), use the trapezoidal rule and all these points to estimate the integral I = integraldisplay 2 0 f ( x ) dx. 1. I 31 4 2. I 17 2 3. I 33 4 correct 4. I 8 5. I 35 4 Explanation: The trapezoidal rule estimates the integral I as h 2 parenleftBig f (0) + 2 f ( 1 2 ) + 2 f (1) + 2 f ( 3 2 ) + f (2) parenrightBig . With h = 1 2 and the given values of f , there- fore, the area is estimated by I 33 4 . 002 10.0points If f is the function whose graph on [0 , 10] is given by 2 4 6 8 2 4 6 8 use the Trapezoidal Rule with n = 5 to esti- mate the integral I = integraldisplay 8 3 f ( x ) dx. 1. I 22 2. I 24 3. I 47 2 4. I 45 2 correct 5. I 23 Explanation: The Trapezoidal Rule estimates the inte- gral I = integraldisplay 8 3 f ( x ) dx by I 1 2 bracketleftBig f (3) + 2 { f (4)+ · · · + f (7) } + f (8) bracketrightBig when n = 5. For the given f , therefore, I 1 2 bracketleftBig 6 + 2 { 5 + 6 + 4 + 3 } + 3 bracketrightBig = 45 2 , reading off the values of f from the graph. keywords: trapezoidal rule, integral, graph

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wei (jw35975) – HW07 – kalahurka – (55230) 2 003 10.0points After partitioning the interval [0 , 4] into 4 equal subintervals, use the trapezoidal rule to
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