equals
15
L is the arc length for t over [a,T]; then compute average speed
16
equals
17
equals
18
this is the signed area between the x-axis and the curve
19
equals
20
make rectangles to visualize area
21
22
0
200
23
equals
2
3
4
5
6
7
8
9
10
11
12
13
14
15
24
equals
25
equals
0.0 6 2 8 3 1 8 5 3 0 7 1 8
0.0 9 4 2 4 7 7 7 9 6 0 7 7
0.1 2 5 6 6 3 7 0 6 1 4 4
0.1 5 7 0 7 9 6 3 2 6 7 9
0.1 8 8 4 9 5 5 5 9 2 1 5
0.2 1 9 9 1 1 4 8 5 7 5 1
0.2 5 1 3 2 7 4 1 2 2 8 7
0.2 8 2 7 4 3 3 3 8 8 2 3
0.3 1 4 1 5 9 2 6 5 3 5 9
0.3 4 5 5 7 5 1 9 1 8 9 5
0.3 7 6 9 9 1 1 1 8 4 3 1
0.4 0 8 4 0 7 0 4 4 9 6 7
0.4 3 9 8 2 2 9 7 1 5 0 3
0.4 7 1 2 3 8 8 9 8 0 3 8
26
equals
negative 0.1 7 9 6 1 2 9 1 5 2 5 4
negative 0.2 3 5 5 3 6 0 4 5 2 4 5
negative 0.2 8 9 4 8 5 2 5 4 3 5 6
negative 0.3 4 1 4 6 0 5 4 2 5 8 7
negative 0.3 9 1 4 6 1 9 0 9 9 3 7
negative 0.4 3 9 4 8 9 3 5 6 4 0 7
negative 0.4 8 5 5 4 2 8 8 1 9 9 7
negative 0.5 2 9 6 2 2 4 8 6 7 0 7
negative 0.5 7 1 7 2 8 1 7 0 5 3 7
negative 0.6 1 1 8 5 9 9 3 3 4 8 6
negative 0.6 5 0 0 1 7 7 7 5 5 5 5
negative 0.6 8 6 2 0 1 6 9 6 7 4 4
negative 0.7 2 0 4 1 1 6 9 7 0 5 2
negative 0.7 5 2 6 4 7 7 7 6 4 8 1
27
equals
negative 0.1 2 1 7 1 5 8 6 4 3 8 3
negative 0.1 7 9 6 1 2 9 1 5 2 5 4
negative 0.2 3 5 5 3 6 0 4 5 2 4 5
negative 0.2 8 9 4 8 5 2 5 4 3 5 6
negative 0.3 4 1 4 6 0 5 4 2 5 8 7
negative 0.3 9 1 4 6 1 9 0 9 9 3 7
negative 0.4 3 9 4 8 9 3 5 6 4 0 7
negative 0.4 8 5 5 4 2 8 8 1 9 9 7
negative 0.5 2 9 6 2 2 4 8 6 7 0 7
negative 0.5 7 1 7 2 8 1 7 0 5 3 7
negative 0.6 1 1 8 5 9 9 3 3 4 8 6
negative 0.6 5 0 0 1 7 7 7 5 5 5 5
negative 0.6 8 6 2 0 1 6 9 6 7 4 4
negative 0.7 2 0 4 1 1 6 9 7 0 5 2
28
29
30
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