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This 2 page Class Notes was uploaded by Mr. Halie Wilkinson on Saturday October 3, 2015. The Class Notes belongs to MT 101 at Boston College taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/218070/mt-101-boston-college in Mathematics (M) at Boston College.
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Date Created: 10/03/15
Prgm INTEGRAL Disp LOWER LIMIT Input 4 Disp UPPER LIMIT Input B Disp DIVNS Input N B lN gt H I gtX39 0 gtL 0 gtM 1 gtI LblP LIM1 gtL X39 517 X39 MLY1 gt M x 5n gt x 15gt LN Goto P Disp LEFTRIGHT Disp L L H 94 Y1 gt R 4 gt X R H 94 Y1 gt R Disp R L R2 gt T Disp TRAPMlDSIMP DispT Disp M 2M T3 gt 539 Disp 539 Where to Find The Commands Disp and Input are accessed via PRGM IO Enter lower limit of integration Enter upper limit of integration Enter number subdivisions Stores size of one subdivisionin I 139 Note that gt means hit STO button Start X off at beginning of interval Initialize L which keeps track ofle sums to zero Initialize M which keeps track of midpoint sums to zero Initialize I the counter for the loop Label for top ofloop Lbl is accessed via PRGM CTL Increment L by Y1 I 139 the area of one more rectangle Y1 is accessed via YVARS or 2nd VARS Move X to middle of interval Evaluate Y1 at the middle of interval and increment M by rectangle of this height Move X to start of next interval L a39 gt is accessed via PRGM CTL This is the most di icult step in the program adds 1 to I and does the the next step if I g N ie if haven t gone through loop enought times otherwise skips next step Thus if I g N goes back to Lbl P and loops through again If I gt N loop is nished and goes on to print out results Continue here if I gt N in which case the value of X is now B Goto is accessed via PRGM CTL Jumps back to Lbl Pif g N L now equals the left sum so display it Add on area of rightmost rectangle store in R Reset X to d Subtract off area of le most rectangle R now equals right sum so display it Trap approximation is average of L and R Display trap approximation Display midpoint approximation Simpson is weighted average of M and T Display Simpson s approximation Lisinxdx 42083 oos0 01 1 APPROXIMATING SUMS n Ln Rn Tn Mn Sn 2 0555 1341 0948 1026 1000134 4 07908 11834 09871 10064 10000082 20 09602 10388 099949 100026 1000000013 ERRORS n Ln Rn Tn Mn Sn 2 445 341 052 026 000134 4 209 183 013 0064 0000082 20 0398 0388 000514 00026 000000013 HOW DO THE ERRORS DECREASE AS THE NUMBER OF SUBINTERVALS INCREASES Let k factor by which we increase n n number of subintervals ERRORS n Ln Rn Tn Mn Sn 2 445 341 052 026 000134 k2 4 209 183 013 0064 0000082 k5 20 0398 0388 000514 00026 000000013
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