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Unformatted text preview: Problem Set CV1 MMAE: 501 Engineering Analysis I Kevin W. Cassel Mechanical, Materials and Aerospace Engineering Department Illinois Institute of Technology 10 West 32nd Street Chicago, IL 60616 email@example.com Problem Reference Problem # 1: Hildebrand, Chapter 2, Problem 4 Problem # 2: Hildebrand, Chapter 2, Problem 10 Problem # 3: Hildebrand, Chapter 2, Problem 9 Problem # 4: Hildebrand, Chapter 2, Problem 16 Problem # 5: Hildebrand, Chapter 2, Problem 17 Problem # 6: Hildebrand, Chapter 2, Problem 20 c 2007 Kevin W. Cassel 1 Problem # 1 Of all parabolas which pass through the points (0 , 0) and (1,1), determine that one which, when rotated about the x axis, generates a solid of revolution with least possible volume between x = 0 and x = 1. [Notice that the equation may be taken in the form y = x + cx (1- x ), where c is to be determined.] Problem # 2 By interchanging the order of integration, show that the extremals of the inte- gral I = Z b a Z t a K ( x,t ) f ( x,y,y ) dxdt satisfy the equation...
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