運算式 33: "G" Subscript, 3 , Baseline left parenthesis, "x" , "n" , right parenthesis equals left brace, "a" plus 2 "n" "q" less than or equal to "x" less than "a" plus 2 "n" "q" plus "q" : "p" left parenthesis, "x" , "a" plus 2 "n" "q" , right parenthesis , 0 , right braceG3x,n=a+2nq≤x<a+2nq+q:px,a+2nq,0
33
運算式 34: "H" Subscript, 1 , Baseline left parenthesis, "x" , "n" , right parenthesis equals left brace, "a" plus 2 "n" "q" plus "q" less than or equal to "x" less than or equal to "a" plus 2 "n" "q" plus 2 "q" : "f" left parenthesis, "a" plus 2 "n" "q" plus "q" plus "c" "q" , right parenthesis , 0 , right braceH1x,n=a+2nq+q≤x≤a+2nq+2q:fa+2nq+q+cq,0
34
運算式 35: "H" Subscript, 2 , Baseline left parenthesis, "x" , "n" , right parenthesis equals left brace, "a" plus 2 "n" "q" plus "q" less than or equal to "x" less than or equal to "a" plus 2 "n" "q" plus 2 "q" : StartFraction, left parenthesis, "f" left parenthesis, "a" plus 2 "n" "q" plus 2 "q" , right parenthesis minus "f" left parenthesis, "a" plus 2 "n" "q" plus "q" , right parenthesis , right parenthesis left parenthesis, "x" minus "a" minus 2 "n" "q" minus "q" , right parenthesis Over "q" , EndFraction plus "f" left parenthesis, "a" plus 2 "n" "q" plus "q" , right parenthesis , 0 , right braceH2x,n=a+2nq+q≤x≤a+2nq+2q:fa+2nq+2q−fa+2nq+qx−a−2nq−qq+fa+2nq+q,0
35
運算式 36: "H" Subscript, 3 , Baseline left parenthesis, "x" , "n" , right parenthesis equals left brace, "a" plus 2 "n" "q" plus "q" less than or equal to "x" less than or equal to "a" plus 2 "n" "q" plus 2 "q" : "p" left parenthesis, "x" , "a" plus 2 "n" "q" plus "q" , right parenthesis , 0 , right braceH3x,n=a+2nq+q≤x≤a+2nq+2q:px,a+2nq+q,0
36
Sets the output piecewise function to the selected method.
37
運算式 38: "G" left parenthesis, "x" , "n" , right parenthesis equals left brace, "A" equals 1 : "G" Subscript, 1 , Baseline left parenthesis, "x" , "n" , right parenthesis , "A" equals 2 : "G" Subscript, 2 , Baseline left parenthesis, "x" , "n" , right parenthesis , "A" equals 3 : "G" Subscript, 3 , Baseline left parenthesis, "x" , "n" , right parenthesis , right braceGx,n=A=1:G1x,n,A=2:G2x,n,A=3:G3x,n
38
運算式 39: "H" left parenthesis, "x" , "n" , right parenthesis equals left brace, "A" equals 1 : "H" Subscript, 1 , Baseline left parenthesis, "x" , "n" , right parenthesis , "A" equals 2 : "H" Subscript, 2 , Baseline left parenthesis, "x" , "n" , right parenthesis , "A" equals 3 : "H" Subscript, 3 , Baseline left parenthesis, "x" , "n" , right parenthesis , right braceHx,n=A=1:H1x,n,A=2:H2x,n,A=3:H3x,n
39
Aggregates the piecewise functions.
40
運算式 41: "g" left parenthesis, "x" , right parenthesis equals left brace, "a" less than "x" less than "b" , right brace Start sum from "n" equals 0 to StartFraction, "N" Over 2 , EndFraction , end sum, "G" left parenthesis, "x" , "n" , right parenthesisgx=a<x<bN2∑n=0Gx,n
41
運算式 42: "h" left parenthesis, "x" , right parenthesis equals left brace, "a" less than "x" less than "b" , right brace Start sum from "n" equals 0 to StartFraction, "N" Over 2 , EndFraction , end sum, "H" left parenthesis, "x" , "n" , right parenthesishx=a<x<bN2∑n=0Hx,n
42
Makes borders between each color 'bar' for Simpson's and Trapezoid rules.
43
運算式 44: left parenthesis, "a" plus "q" plus floor left parenthesis, "M" "t" , right parenthesis "q" , mod left parenthesis, "M" "t" , 1 , right parenthesis "f" left parenthesis, "a" plus "q" plus floor left parenthesis, "M" "t" , right parenthesis "q" , right parenthesis left brace, "A" equals 2 , "A" equals 3 , right brace left brace, "b" greater than "a" , right brace , right parenthesisa+q+floorMtq,modMt,1fa+q+floorMtqA=2,A=3b>a
44
Makes borders between each color bar for Riemann sums.
45
運算式 46: left parenthesis, "a" plus "q" plus floor left parenthesis, "M" "t" , right parenthesis "q" , "m" Subscript, "o" , Baseline left parenthesis, "t" , right parenthesis left parenthesis, "C" left parenthesis, "f" Subscript, "l" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis "T" left parenthesis, "f" Subscript, "l" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesis plus left parenthesis, 1 minus "C" left parenthesis, "f" Subscript, "l" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesis left parenthesis, "f" left parenthesis, "a" plus "q" "f" Subscript, "l" , Baseline left parenthesis, "t" , right parenthesis plus "c" "q" , right parenthesis left parenthesis, 1 minus "m" Subscript, "o" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis plus "m" Subscript, "o" , Baseline left parenthesis, "t" , right parenthesis "f" left parenthesis, "a" plus "q" "f" Subscript, "l" , Baseline left parenthesis, "t" , right parenthesis plus "q" plus "c" "q" , right parenthesis , right parenthesis left brace, "A" equals 1 , right brace left brace, "b" greater than "a" , right brace , right parenthesisa+q+floorMtq,motCfltTflt+1−Cfltfa+qflt+cq1−mot+motfa+qflt+q+cqA=1b>a
46
The next five lines are abbreviations used for the equation above:
47
運算式 48: "f" Subscript, "l" , Baseline left parenthesis, "t" , right parenthesis equals floor left parenthesis, "M" "t" , right parenthesisflt=floorMt
48
運算式 49: "m" Subscript, "o" , Baseline left parenthesis, "t" , right parenthesis equals mod left parenthesis, "M" "t" , 1 , right parenthesismot=modMt,1
49
運算式 50: "C" left parenthesis, "n" , right parenthesis equals .5signum left parenthesis, "f" left parenthesis, "a" plus "q" "n" plus "c" "q" , right parenthesis "f" left parenthesis, "a" plus "q" "n" plus "q" plus "c" "q" , right parenthesis , right parenthesis plus .5Cn=.5signfa+qn+cqfa+qn+q+cq+.5
50
運算式 51: "T" left parenthesis, "n" , right parenthesis equals signum left parenthesis, "f" left parenthesis, "a" plus "q" "n" plus "c" "q" , right parenthesis , right parenthesis max left parenthesis, StartAbsoluteValue, "f" left parenthesis, "a" plus "q" "n" plus "c" "q" , right parenthesis , EndAbsoluteValue , StartAbsoluteValue, "f" left parenthesis, "a" plus "q" "n" plus "q" plus "c" "q" , right parenthesis , EndAbsoluteValue , right parenthesisTn=signfa+qn+cqmaxfa+qn+cq,fa+qn+q+cq
51
運算式 52: "M" equals "N" minus 1M=N−1
52
Adds a border to the end of the shaded region.
53
運算式 54: left parenthesis, "a" , "f" left parenthesis, "a" plus "q" "c" left brace, "A" equals 1 , 0 , right brace , right parenthesis "t" left brace, "b" greater than or equal to "a" , right brace , right parenthesisa,fa+qcA=1,0tb≥a
54
運算式 55: left parenthesis, "b" , "f" left parenthesis, "b" plus left parenthesis, negative "q" plus "q" "c" , right parenthesis left brace, "A" equals 1 , 0 , right brace , right parenthesis "t" left brace, "b" greater than "a" , right brace , right parenthesisb,fb+−q+qcA=1,0tb>a
55
Calculates the value of the integral using Simpson's Rule and m (preset to 100) partitions.
56
運算式 57: "I" equals StartFraction, "Q" Over 3 , EndFraction left parenthesis, .5 left parenthesis, "f" left parenthesis, "b" , right parenthesis minus "f" left parenthesis, "a" , right parenthesis , right parenthesis plus Start sum from "n" equals 0 to "m" minus 1, end sum, left parenthesis, "f" left parenthesis, "a" plus "n" "Q" , right parenthesis plus 2 "f" left parenthesis, "a" plus left parenthesis, "n" plus .5 , right parenthesis "Q" , right parenthesis , right parenthesis , right parenthesisI=Q3.5fb−fa+m−1∑n=0fa+nQ+2fa+n+.5Q
57
運算式 58: "m" equals 100m=100
58
運算式 59: "Q" equals StartFraction, left parenthesis, "b" minus "a" , right parenthesis Over "m" , EndFractionQ=b−am
59
Creates a quadratic model for each partition (needed for Simpson's rule graph)
60
運算式 61: "p" left parenthesis, "t" , "s" , right parenthesis equals left parenthesis, .5 "f" left parenthesis, "s" , right parenthesis minus "f" left parenthesis, "s" plus .5 "q" , right parenthesis plus .5 "f" left parenthesis, "s" plus "q" , right parenthesis , right parenthesis left parenthesis, StartFraction, 2 left parenthesis, "t" minus "s" , right parenthesis Over "q" , EndFraction , right parenthesis squared plus left parenthesis, negative 1.5 "f" left parenthesis, "s" , right parenthesis plus 2 "f" left parenthesis, "s" plus .5 "q" , right parenthesis minus 0.5 "f" left parenthesis, "s" plus "q" , right parenthesis , right parenthesis left parenthesis, StartFraction, 2 left parenthesis, "t" minus "s" , right parenthesis Over "q" , EndFraction , right parenthesis plus "f" left parenthesis, "s" , right parenthesispt,s=.5fs−fs+.5q+.5fs+q2t−sq2+−1.5fs+2fs+.5q−0.5fs+q2t−sq+fs
61
Sets the expected integration value to suit the selected method.
62
運算式 63: "E" equals left brace, "A" equals 1 : "E" Subscript, 1 , Baseline , "A" equals 2 : "E" Subscript, 2 , Baseline , "E" Subscript, 3 , Baseline , right braceE=A=1:E1,A=2:E2,E3
