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07.06.1 Chapter 07.06 Gauss Quadrature Rule for Integration-More Examples Mechanical Engineering Example 1 A trunnion of diameter 3 36 . 12 has to be cooled from a room temperature of F 80 before it is shrink fit into a steel hub (Figure 1). Figure 1 Trunnion to be slid through the hub after contracting. The equation that gives the diametric contraction, in inches of the trunnion in dry-ice/alcohol (boiling temperature is F 108 ) is given by: 108 80 6 9 2 11 10 015 . 6 10 1946 . 6 10 2278 . 1 363 . 12 dT T T D a) Use two-point Gauss Quadrature Rule to find the contraction. b) Find the absolute relative true error. Solution a) First, change the limits of integration from 108 , 80 to 1 , 1 using 1 1 2 2 2 ) ( 108 80 dT a b T a b f a b dT T f b a b a gives

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07.06.2 Chapter 07.06 1 1 108 80 2 80 108 2 80 108 2 80 108 ) ( dT T f dT T f 1 1 14 94 94 dT T f
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