MAT 232-Calc-1-A6 - A = 4/5 26 (x) = 3 (x 1), g(x) = x 1 3...

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Calculus I Calculus: Early Transcendental Functions , 4th ed., by Ron Larson, Robert Hostetler, and Bruce H. Edwards (Boston: Houghton Mifflin, 2007; ISBN-10: 0-618-60624-6). Written Assignment 6 The written assignment draws on even-numbered exercises from the textbook. Answer all assigned exercises, and show all work. Section Exercises 7.1 2, 4, 6, 8, 12, 20, 22, 24, 26, 28, 30, 32, 34, 36, 40, 44, 50 #20 Sketch the region bounded by the graphs of the algebraic functions and find the area of the region. ƒ(x) = -x 2 + 4x + 1, g(x) = x + 1 -x 2 + 4x + 1 = x + 1 => x 2 - 3x = 0 => x(x – 3) = => x = 0, 3 g(x) ≤ ƒ(x) for 0≤ x ≤ 3 Area = ƒ 0 3 [(-x 2 + 4x + 1) – (x + 1)]dx Area = ƒ 0 3 [(-x 2 + 4x + 1 - x - 1)]dx Area = ƒ 0 3 (-x 2 + 3x) dx = [-(x 3 /3) + (3/2)x 2 ] 0 3 = - 9 + 27/2 A = 9/2 24 y = 1/x 2 , y = 0, x = 1, x = 5 1/x 2 ≥ 0 for x A = ƒ 1 5 (1/x 2 ) dx A = ƒ 1 5 x 2 dx A = [-x -1 ] 1 5 A = [-1/ x 1 ] 1 5 A = [-1/ 5 + 1]
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Unformatted text preview: A = 4/5 26 (x) = 3 (x 1), g(x) = x 1 3 (x 1) = x 1 (x 1) = (x 1) 3 Intersection points x = 0, 1, 2 A = 1 [(x 1) ( x - 1) 1/3 ]dx + 1 2 [(x 1) 1/3 ( x - 1)]dx A = [(x 1) 2 /2 3/4( x - 1) 4/3 ] 1 + [3/4(x 1) 4/3 ( x - 1) 2 /2] 1 2 A = 1/2 - + - A = 0 28 (y) = y(2 y) , g(y) = -y y(2 y) = -y y(3 y) = 0 y = 0,3 A = 3 [(y) g(y)]dy A = 3 [y(2 y) (-y)]dy A = 3 (3y y 2 )dy A = ((3/2)y 2 (1/3)y 3 ) 3 A = 27/2 9 A = 9/2 30 (y) = y/(16 y 2 ), g(y) = 0, y = 3 A = 3 (y/(16 y 2 ) dy 16 y 2 = t therefore, -2ydy = dt when y = 0, t = 16 Then y = 3, t = 7 A = -1/2 16 7 t-1/2 dt A = -1/2 [2t 1/2 ] 16 7 A = - [t] 16 7 A = -7 +4 A = 4 - 7...
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This note was uploaded on 09/29/2010 for the course MAT MAT 231 taught by Professor Hannah during the Spring '10 term at Thomas Edison State.

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MAT 232-Calc-1-A6 - A = 4/5 26 (x) = 3 (x 1), g(x) = x 1 3...

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