HW07-solutions - wei (jw35975) – HW07 – kalahurka –...

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Unformatted text preview: 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 10.0 points 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 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 10.0 points 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....
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This note was uploaded on 03/26/2012 for the course MATH 408 L taught by Professor Zheng during the Spring '10 term at University of Texas at Austin.

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HW07-solutions - wei (jw35975) – HW07 – kalahurka –...

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