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07.06.1 Chapter 07.06 Gauss Quadrature Rule for Integration-More Examples Industrial Engineering Example 1 A company advertises that every roll of toilet paper has at least 250 sheets. The probability that there are 250 or more sheets in the toilet paper is given by 250 ) 2 . 252 ( 3881 . 0 2 3515 . 0 ) 250 ( dy e y P y Approximating the above integral as 270 250 ) 2 . 252 ( 3881 . 0 2 3515 . 0 ) 250 ( dy e y P y a) Use two-point Gauss Quadrature Rule to find the probability. b) Find the absolute relative true error. Solution a) First, change the limits of integration from   270 , 250 to   1 , 1 using 1 1 2 2 2 ) ( 270 250 dy a b y a b f a b dy y f b a b a gives 1 1 270 250 2 250 270 2 250 270 2 250 270 ) ( dy y f dy y f  1 1 260 10 10 dy y f Next, get weighting factors and function argument values for the two point rule, 0000 . 1 1 c 57735 . 0

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