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mws_ind_int_txt_romberg_examples

# mws_ind_int_txt_romberg_examples - Chapter 07.05 Romberg...

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Chapter 07.05 Romberg 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 Table 1 Values obtained using Trapezoidal rule. n Trapezoidal Rule 1 2 4 8 0.53721 0.26861 0.21814 0.95767 a) Use Romberg’s rule to find the probability. Use the 2-segment and 4-segment Trapezoidal rule results given in Table 1. b) Find the true error, t E , for part (a). c) Find the absolute relative true error, t ,for part (a). Solution a) 26861 . 0 2 I 21814 . 0 4 I Using Richardson’s extrapolation formula for Trapezoidal rule 3 2 2 n n n I I I TV and choosing 2 n , 3 2 4 4 I I I TV 3 26861 . 0 21814 . 0 21814

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mws_ind_int_txt_romberg_examples - Chapter 07.05 Romberg...

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