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07.06.1 07.06 Gauss Quadrature Rule for Integration-More Examples Chemical Engineering Example 1 In an attempt to understand the mechanism of the depolarization process in a fuel cell, an electro-kinetic model for mixed oxygen-methanol current on platinum was developed in the laboratory at FAMU. A very simplified model of the reaction developed suggests a functional relation in an integral form. To find the time required for 50% of the oxygen to be consumed, the time,   s T is given by dx x x T 6 6 10 61 . 0 10 22 . 1 11 7 10 316 . 2 10 3025 . 4 73 . 6 Use two-point Gauss quadrature rule to find the time required for 50 % of the oxygen to be consumed. Also, find the absolute relative true error. Solution First, change the limits of integration from 6 6 10 61 . 0 , 10 22 . 1 to 1 , 1 using 1 1 2 2 2 ) ( dx a b x a b f a b dx x f b a gives 1 1 6 6 6 6 6 6 10 61 . 0 10 22 . 1 2 10 22 . 1 10 61 . 0 2 10 22 . 1 10 61 . 0 2 10 22 . 1 10 61 . 0 ) ( 6 6 dx x f dx x f 1 1 6 6 6 10 91500 . 0 10 05 . 3 10 305 . 0 dx x f Next, get weighting factors and function argument values from Table 1 for the two point rule, 0000 . 1 1 c

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