Expression 15: "s" left parenthesis, "a" , right parenthesissa
equals=
4.3 9 8 3 7 2 0 1 4 2 44.39837201424
15
L is the arc length for t over [a,T]; then compute average speed
16
Expression 17: "L" equals Start integral from "T" Subscript, 0 , Baseline to "a" , end integral, "s" left parenthesis, "t" , right parenthesis "d" "t"L=∫aT0stdt
equals=
6.1 2 6 1 7 8 4 8 0 3 66.12617848036
17
Expression 18: StartFraction, "L" Over "a" minus "T" Subscript, 0 , Baseline , EndFractionLa−T0
equals=
1.9 5 0 0 2 3 1 7 4 8 21.95002317482
18
this is the signed area between the x-axis and the curve
19
Expression 20: "A" equals Start integral from "T" Subscript, 0 , Baseline to "a" , end integral, "g" left parenthesis, "t" , right parenthesis StartFraction, "d" Over "d" "t" , EndFraction "f" left parenthesis, "t" , right parenthesis "d" "t"A=∫aT0gtddtftdt
equals=
2.2 8 3 1 8 5 3 0 7 1 82.28318530718
20
make rectangles to visualize area
21
Expression 22: 0 less than or equal to "y" less than or equal to "g" left parenthesis, "P" , right parenthesis left brace, "x" Subscript, 0 , Baseline less than "x" less than "x" Subscript, 1 , Baseline , right brace0≤y≤gPx0<x<x1
22
Expression 23: "N" equals 100N=100
00
200200
23
Expression 24: "k" equals left bracket, 1... "N" , right bracketk=1...N
equals=
11
22
33
44
55
66
77
88
99
1010
1111
1212
1313
1414
1515
100 element list
24
Expression 25: "d" equals StartFraction, left parenthesis, "a" minus "T" Subscript, 0 , Baseline , right parenthesis Over "N" , EndFractiond=a−T0N
equals=
0.0 3 1 4 1 5 9 2 6 5 3 5 90.0314159265359
25
Expression 26: "P" equals "k" times "d"P=k·d
equals=
0.0 3 1 4 1 5 9 2 6 5 3 5 90.0314159265359
0.0 6 2 8 3 1 8 5 3 0 7 1 80.0628318530718
0.0 9 4 2 4 7 7 7 9 6 0 7 70.0942477796077
0.1 2 5 6 6 3 7 0 6 1 4 40.125663706144
0.1 5 7 0 7 9 6 3 2 6 7 90.157079632679
0.1 8 8 4 9 5 5 5 9 2 1 50.188495559215
0.2 1 9 9 1 1 4 8 5 7 5 10.219911485751
0.2 5 1 3 2 7 4 1 2 2 8 70.251327412287
0.2 8 2 7 4 3 3 3 8 8 2 30.282743338823
0.3 1 4 1 5 9 2 6 5 3 5 90.314159265359
0.3 4 5 5 7 5 1 9 1 8 9 50.345575191895
0.3 7 6 9 9 1 1 1 8 4 3 10.376991118431
0.4 0 8 4 0 7 0 4 4 9 6 70.408407044967
0.4 3 9 8 2 2 9 7 1 5 0 30.439822971503
0.4 7 1 2 3 8 8 9 8 0 3 80.471238898038
100 element list
26
Expression 27: "x" Subscript, 0 , Baseline equals min left parenthesis, "f" left parenthesis, "P" , right parenthesis , "f" left parenthesis, "P" plus "d" , right parenthesis , right parenthesisx0=minfP,fP+d
equals=
negative 0.1 2 1 7 1 5 8 6 4 3 8 3−0.121715864383
negative 0.1 7 9 6 1 2 9 1 5 2 5 4−0.179612915254
negative 0.2 3 5 5 3 6 0 4 5 2 4 5−0.235536045245
negative 0.2 8 9 4 8 5 2 5 4 3 5 6−0.289485254356
negative 0.3 4 1 4 6 0 5 4 2 5 8 7−0.341460542587
negative 0.3 9 1 4 6 1 9 0 9 9 3 7−0.391461909937
negative 0.4 3 9 4 8 9 3 5 6 4 0 7−0.439489356407
negative 0.4 8 5 5 4 2 8 8 1 9 9 7−0.485542881997
negative 0.5 2 9 6 2 2 4 8 6 7 0 7−0.529622486707
negative 0.5 7 1 7 2 8 1 7 0 5 3 7−0.571728170537
negative 0.6 1 1 8 5 9 9 3 3 4 8 6−0.611859933486
negative 0.6 5 0 0 1 7 7 7 5 5 5 5−0.650017775555
negative 0.6 8 6 2 0 1 6 9 6 7 4 4−0.686201696744
negative 0.7 2 0 4 1 1 6 9 7 0 5 2−0.720411697052
negative 0.7 5 2 6 4 7 7 7 6 4 8 1−0.752647776481
100 element list
27
Expression 28: "x" Subscript, 1 , Baseline equals max left parenthesis, "f" left parenthesis, "P" , right parenthesis , "f" left parenthesis, "P" plus "d" , right parenthesis , right parenthesisx1=maxfP,fP+d