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07.06.1 07.06 Gauss Quadrature Rule for Integration-More Examples Civil Engineering Example 1 The concentration of benzene at a critical location is given by      758 . 5 6560 . 0 75 . 1 73 . 32 erfc e erfc c where dz e x erfc x z 2 So in the above formula dz e erfc z 6560 . 0 2 6560 . 0 Since 2 z e decays rapidly as z , we will approximate 6560 . 0 5 2 6560 . 0 dz e erfc z a) Use two-point Gauss Quadrature Rule to approximate the value of 6560 . 0 erfc . b) Find the absolute relative true error for part (a). Solution a) First, change the limits of integration from   6560 . 0 , 5 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 6560 . 0 5 2 5 6560 . 0 2 5 6560 . 0 2 5 6560 . 0 ) ( dz z f dz z f 1 1 8280 . 2 1720 . 2 1720 . 2 dz z f Next, get weighting factors and function argument values for the two point rule, 0000 . 1 1 c 57735 . 0

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