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Important: Macros must be enabled, otherwise the grapher wi* This improved and expanded version of the grapher is due to Jeff Morgan, Department of Mathe

This set of worksheets will automatically graph any function of x, show the (left) Riemann sum as a shaded aUse the tabs at the bottom of the sheet to switch to the right sum grapher, or the midpoint sum grapher (whi

Instructions: Just enter the function in cell G13 (as shown; no equals sign) enter values for the limits of inteand a value between 1 and 200 for the number of partitions n.

Notes: The number of partitions n cannot exceed 200 for this grapher Function: x^2Do not change the value of the Riemann Sum in cell I15. a: 0

The graph data is hidden on the right b: 1

00.03

0.050.08

0.10.13

0.150.18

0.20.23

0.250.28

0.30.33

0.350.38

0.40.43

0.450.48

0.50.53

0.550.58

0.60.63

0.650.68

0.70.73

0.750.78

0.80.83

0.850.88

0.90.93

0.950.98

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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Dont touch this table!x y u y_u

0 0 0 0

ll not work. 0.01 0 0 0atics, Texas A&M University. 0.01 0 0 0

rea, and also ita value. 0.02 0 0 0och also shows the trapeziod sum). 0.02 0 0 0

0.03 0 0 0gration a and b, 0.03 0 0 0

0.04 0 0 00.04 0 0 00.05 0 0 0

0.05 0 0 0

n: 10 0.06 0 0 00.06 0 0 00.06 0 0 0

0.07 0 0 00.08 0.01 0 00.08 0.01 0 00.09 0.01 0 00.09 0.01 0 0

0.1 0.01 0 00.1 0.01 0.1 0.01

0.11 0.01 0.1 0.010.11 0.01 0.1 0.01

Left Sum 0.12 0.01 0.1 0.010.29 0.12 0.01 0.1 0.01

0.13 0.02 0.1 0.010.13 0.02 0.1 0.01

pi 0.14 0.02 0.1 0.013.14 0.14 0.02 0.1 0.01

e 0.15 0.02 0.1 0.012.72 0.15 0.02 0.1 0.01

0.16 0.02 0.1 0.010.16 0.03 0.1 0.010.17 0.03 0.1 0.010.17 0.03 0.1 0.010.18 0.03 0.1 0.010.18 0.03 0.1 0.010.19 0.03 0.1 0.010.19 0.04 0.1 0.01

0.2 0.04 0.1 0.010.2 0.04 0.2 0.04

0.21 0.04 0.2 0.040.21 0.04 0.2 0.040.22 0.05 0.2 0.040.22 0.05 0.2 0.04

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0.23 0.05 0.2 0.040.23 0.05 0.2 0.040.24 0.06 0.2 0.040.24 0.06 0.2 0.040.25 0.06 0.2 0.040.25 0.06 0.2 0.04

0.26 0.07 0.2 0.040.26 0.07 0.2 0.040.27 0.07 0.2 0.040.27 0.07 0.2 0.040.28 0.08 0.2 0.040.28 0.08 0.2 0.040.29 0.08 0.2 0.040.29 0.08 0.2 0.04

0.3 0.09 0.2 0.040.3 0.09 0.3 0.09

0.31 0.09 0.3 0.090.31 0.1 0.3 0.090.32 0.1 0.3 0.090.32 0.1 0.3 0.090.33 0.11 0.3 0.090.33 0.11 0.3 0.090.34 0.11 0.3 0.090.34 0.12 0.3 0.090.35 0.12 0.3 0.090.35 0.12 0.3 0.090.36 0.13 0.3 0.090.36 0.13 0.3 0.090.37 0.13 0.3 0.090.37 0.14 0.3 0.090.38 0.14 0.3 0.090.38 0.14 0.3 0.090.39 0.15 0.3 0.090.39 0.15 0.3 0.09

0.4 0.16 0.3 0.090.4 0.16 0.4 0.16

0.41 0.16 0.4 0.160.41 0.17 0.4 0.160.42 0.17 0.4 0.160.42 0.18 0.4 0.160.43 0.18 0.4 0.160.43 0.18 0.4 0.160.44 0.19 0.4 0.160.44 0.19 0.4 0.160.45 0.2 0.4 0.160.45 0.2 0.4 0.160.46 0.21 0.4 0.160.46 0.21 0.4 0.160.47 0.22 0.4 0.160.47 0.22 0.4 0.16

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0.48 0.23 0.4 0.160.48 0.23 0.4 0.160.49 0.24 0.4 0.160.49 0.24 0.4 0.16

0.5 0.25 0.4 0.160.5 0.25 0.5 0.25

0.51 0.26 0.5 0.250.51 0.26 0.5 0.250.52 0.27 0.5 0.250.52 0.27 0.5 0.250.53 0.28 0.5 0.250.53 0.28 0.5 0.250.54 0.29 0.5 0.250.54 0.29 0.5 0.250.55 0.3 0.5 0.250.55 0.3 0.5 0.250.56 0.31 0.5 0.250.56 0.31 0.5 0.250.57 0.32 0.5 0.250.57 0.32 0.5 0.250.58 0.33 0.5 0.250.58 0.34 0.5 0.250.59 0.34 0.5 0.250.59 0.35 0.5 0.25

0.6 0.35 0.5 0.250.6 0.36 0.6 0.36

0.61 0.37 0.6 0.360.61 0.37 0.6 0.360.62 0.38 0.6 0.360.62 0.38 0.6 0.360.63 0.39 0.6 0.360.63 0.4 0.6 0.360.64 0.4 0.6 0.360.64 0.41 0.6 0.360.65 0.42 0.6 0.360.65 0.42 0.6 0.360.66 0.43 0.6 0.360.66 0.44 0.6 0.360.67 0.44 0.6 0.360.67 0.45 0.6 0.360.68 0.46 0.6 0.36

0.68 0.46 0.6 0.360.69 0.47 0.6 0.360.69 0.48 0.6 0.36

0.7 0.48 0.6 0.360.7 0.49 0.7 0.49

0.71 0.5 0.7 0.490.71 0.5 0.7 0.490.72 0.51 0.7 0.490.72 0.52 0.7 0.49

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0.73 0.53 0.7 0.490.73 0.53 0.7 0.490.74 0.54 0.7 0.490.74 0.55 0.7 0.490.75 0.56 0.7 0.490.75 0.56 0.7 0.49

0.76 0.57 0.7 0.490.76 0.58 0.7 0.490.77 0.59 0.7 0.490.77 0.59 0.7 0.490.78 0.6 0.7 0.490.78 0.61 0.7 0.490.79 0.62 0.7 0.490.79 0.62 0.7 0.49

0.8 0.63 0.7 0.490.8 0.64 0.8 0.64

0.81 0.65 0.8 0.640.81 0.66 0.8 0.640.82 0.66 0.8 0.640.82 0.67 0.8 0.640.83 0.68 0.8 0.640.83 0.69 0.8 0.640.84 0.7 0.8 0.640.84 0.71 0.8 0.640.85 0.71 0.8 0.640.85 0.72 0.8 0.640.86 0.73 0.8 0.640.86 0.74 0.8 0.640.87 0.75 0.8 0.640.87 0.76 0.8 0.640.88 0.77 0.8 0.640.88 0.77 0.8 0.640.89 0.78 0.8 0.640.89 0.79 0.8 0.64

0.9 0.8 0.8 0.640.9 0.81 0.9 0.81

0.91 0.82 0.9 0.810.91 0.83 0.9 0.810.92 0.84 0.9 0.810.92 0.85 0.9 0.810.93 0.86 0.9 0.81

0.93 0.86 0.9 0.810.94 0.87 0.9 0.810.94 0.88 0.9 0.810.95 0.89 0.9 0.810.95 0.9 0.9 0.810.96 0.91 0.9 0.810.96 0.92 0.9 0.810.97 0.93 0.9 0.810.97 0.94 0.9 0.81

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0.98 0.95 0.9 0.810.98 0.96 0.9 0.810.99 0.97 0.9 0.810.99 0.98 0.9 0.81

1 0.99 0.9 0.811 1 1 0.81

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0.1 p q r s0.01 0 0 0 0

1 0.1 0.01 0.012 0.2 0.04 0.04

3 0.3 0.09 0.094 0.4 0.16 0.165 0.5 0.25 0.256 0.6 0.36 0.367 0.7 0.49 0.498 0.8 0.64 0.649 0.9 0.81 0.81

10 1 1 0

11 1.1 1.21 0

12 1.2 1.44 013 1.3 1.69 0

14 1.4 1.96 015 1.5 2.25 016 1.6 2.56 017 1.7 2.89 018 1.8 3.24 019 1.9 3.61 020 2 4 021 2.1 4.41 022 2.2 4.84 0

23 2.3 5.29 0

24 2.4 5.76 025 2.5 6.25 026 2.6 6.76 0

27 2.7 7.29 0

28 2.8 7.84 0

29 2.9 8.41 0

30 3 9 031 3.1 9.61 032 3.2 10.24 033 3.3 10.89 034 3.4 11.56 035 3.5 12.25 036 3.6 12.96 037 3.7 13.69 038 3.8 14.44 039 3.9 15.21 040 4 16 041 4.1 16.81 042 4.2 17.64 043 4.3 18.49 044 4.4 19.36 0

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45 4.5 20.25 046 4.6 21.16 047 4.7 22.09 048 4.8 23.04 049 4.9 24.01 050 5 25 0

51 5.1 26.01 052 5.2 27.04 053 5.3 28.09 054 5.4 29.16 055 5.5 30.25 056 5.6 31.36 057 5.7 32.49 058 5.8 33.64 059 5.9 34.81 060 6 36 061 6.1 37.21 062 6.2 38.44 063 6.3 39.69 064 6.4 40.96 065 6.5 42.25 066 6.6 43.56 067 6.7 44.89 068 6.8 46.24 069 6.9 47.61 070 7 49 071 7.1 50.41 072 7.2 51.84 073 7.3 53.29 074 7.4 54.76 075 7.5 56.25 076 7.6 57.76 077 7.7 59.29 078 7.8 60.84 079 7.9 62.41 080 8 64 081 8.1 65.61 082 8.2 67.24 083 8.3 68.89 084 8.4 70.56 085 8.5 72.25 086 8.6 73.96 087 8.7 75.69 088 8.8 77.44 089 8.9 79.21 090 9 81 091 9.1 82.81 092 9.2 84.64 093 9.3 86.49 094 9.4 88.36 0

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95 9.5 90.25 096 9.6 92.16 097 9.7 94.09 098 9.8 96.04 099 9.9 98.01 0

100 10 100 0

101 10.1 102.01 0102 10.2 104.04 0103 10.3 106.09 0104 10.4 108.16 0105 10.5 110.25 0106 10.6 112.36 0107 10.7 114.49 0108 10.8 116.64 0109 10.9 118.81 0110 11 121 0111 11.1 123.21 0112 11.2 125.44 0113 11.3 127.69 0114 11.4 129.96 0115 11.5 132.25 0116 11.6 134.56 0117 11.7 136.89 0118 11.8 139.24 0119 11.9 141.61 0120 12 144 0121 12.1 146.41 0122 12.2 148.84 0123 12.3 151.29 0124 12.4 153.76 0125 12.5 156.25 0126 12.6 158.76 0127 12.7 161.29 0128 12.8 163.84 0129 12.9 166.41 0130 13 169 0131 13.1 171.61 0132 13.2 174.24 0133 13.3 176.89 0134 13.4 179.56 0135 13.5 182.25 0

136 13.6 184.96 0137 13.7 187.69 0138 13.8 190.44 0139 13.9 193.21 0140 14 196 0141 14.1 198.81 0142 14.2 201.64 0143 14.3 204.49 0144 14.4 207.36 0

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145 14.5 210.25 0146 14.6 213.16 0147 14.7 216.09 0148 14.8 219.04 0149 14.9 222.01 0150 15 225 0

151 15.1 228.01 0152 15.2 231.04 0153 15.3 234.09 0154 15.4 237.16 0155 15.5 240.25 0156 15.6 243.36 0157 15.7 246.49 0158 15.8 249.64 0159 15.9 252.81 0160 16 256 0161 16.1 259.21 0162 16.2 262.44 0163 16.3 265.69 0164 16.4 268.96 0165 16.5 272.25 0166 16.6 275.56 0167 16.7 278.89 0168 16.8 282.24 0169 16.9 285.61 0170 17 289 0171 17.1 292.41 0172 17.2 295.84 0173 17.3 299.29 0174 17.4 302.76 0175 17.5 306.25 0176 17.6 309.76 0177 17.7 313.29 0178 17.8 316.84 0179 17.9 320.41 0180 18 324 0181 18.1 327.61 0182 18.2 331.24 0183 18.3 334.89 0184 18.4 338.56 0185 18.5 342.25 0

186 18.6 345.96 0187 18.7 349.69 0188 18.8 353.44 0189 18.9 357.21 0190 19 361 0191 19.1 364.81 0192 19.2 368.64 0193 19.3 372.49 0194 19.4 376.36 0

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195 19.5 380.25 0196 19.6 384.16 0197 19.7 388.09 0198 19.8 392.04 0199 19.9 396.01 0200 20 7200 0

8/8/2019 RiemannSum

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Important: Macros must be enabled, otherwise the grapher wi* This improved and expanded version of the grapher is due to Jeff Morgan, Department of Mathe

This worksheet will automatically graph any function of x, show the (right) Riemann sum as a shaded area, a

Instructions: Just enter the function in cell G13 (as shown; no equals sign) enter values for the limits of inteand a value between 1 and 200 for the number of partitions n.

Notes: The number of partitions n cannot exceed 200 for this grapher Function: x^2Do not change the value of the Riemann Sum in cell I15. a: 0

The graph data is hidden on the right b: 1

00.03

0.050.08

0.10.13

0.150.18

0.20.23

0.250.28

0.30.33

0.350.38

0.40.43

0.450.48

0.50.53

0.550.58

0.60.63

0.650.68

0.70.73

0.750.78

0.80.83

0.850.88

0.90.93

0.950.98

1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

8/8/2019 RiemannSum

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Dont touch this table!x y u y_u

0 0 0.1 0.01

ll not work. 0.01 0 0.1 0.01atics, Texas A&M University. 0.01 0 0.1 0.01

0.02 0 0.1 0.01d also ita value. 0.02 0 0.1 0.01

0.03 0 0.1 0.01gration a and b, 0.03 0 0.1 0.01

0.04 0 0.1 0.010.04 0 0.1 0.010.05 0 0.1 0.01

0.05 0 0.1 0.01

n: 10 0.06 0 0.1 0.010.06 0 0.1 0.010.06 0 0.1 0.010.07 0 0.1 0.010.08 0.01 0.1 0.010.08 0.01 0.1 0.010.09 0.01 0.1 0.010.09 0.01 0.1 0.01

0.1 0.01 0.1 0.010.1 0.01 0.2 0.04

0.11 0.01 0.2 0.040.11 0.01 0.2 0.04

Right Sum 0.12 0.01 0.2 0.040.39 0.12 0.01 0.2 0.04

0.13 0.02 0.2 0.04

pi 0.13 0.02 0.2 0.043.14 0.14 0.02 0.2 0.04

e 0.14 0.02 0.2 0.042.72 0.15 0.02 0.2 0.04

0.15 0.02 0.2 0.040.16 0.02 0.2 0.040.16 0.03 0.2 0.040.17 0.03 0.2 0.040.17 0.03 0.2 0.040.18 0.03 0.2 0.040.18 0.03 0.2 0.04

0.19 0.03 0.2 0.040.19 0.04 0.2 0.04

0.2 0.04 0.2 0.040.2 0.04 0.3 0.09

0.21 0.04 0.3 0.090.21 0.04 0.3 0.090.22 0.05 0.3 0.090.22 0.05 0.3 0.09

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0.23 0.05 0.3 0.090.23 0.05 0.3 0.090.24 0.06 0.3 0.090.24 0.06 0.3 0.090.25 0.06 0.3 0.090.25 0.06 0.3 0.09

0.26 0.07 0.3 0.090.26 0.07 0.3 0.090.27 0.07 0.3 0.090.27 0.07 0.3 0.090.28 0.08 0.3 0.090.28 0.08 0.3 0.090.29 0.08 0.3 0.090.29 0.08 0.3 0.09

0.3 0.09 0.3 0.090.3 0.09 0.4 0.16

0.31 0.09 0.4 0.160.31 0.1 0.4 0.160.32 0.1 0.4 0.160.32 0.1 0.4 0.160.33 0.11 0.4 0.160.33 0.11 0.4 0.160.34 0.11 0.4 0.160.34 0.12 0.4 0.160.35 0.12 0.4 0.160.35 0.12 0.4 0.160.36 0.13 0.4 0.160.36 0.13 0.4 0.160.37 0.13 0.4 0.160.37 0.14 0.4 0.160.38 0.14 0.4 0.160.38 0.14 0.4 0.160.39 0.15 0.4 0.160.39 0.15 0.4 0.16

0.4 0.16 0.4 0.160.4 0.16 0.5 0.25

0.41 0.16 0.5 0.250.41 0.17 0.5 0.250.42 0.17 0.5 0.250.42 0.18 0.5 0.250.43 0.18 0.5 0.250.43 0.18 0.5 0.250.44 0.19 0.5 0.250.44 0.19 0.5 0.250.45 0.2 0.5 0.250.45 0.2 0.5 0.250.46 0.21 0.5 0.250.46 0.21 0.5 0.250.47 0.22 0.5 0.250.47 0.22 0.5 0.25

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0.48 0.23 0.5 0.250.48 0.23 0.5 0.250.49 0.24 0.5 0.250.49 0.24 0.5 0.25

0.5 0.25 0.5 0.250.5 0.25 0.6 0.36

0.51 0.26 0.6 0.360.51 0.26 0.6 0.360.52 0.27 0.6 0.360.52 0.27 0.6 0.360.53 0.28 0.6 0.360.53 0.28 0.6 0.360.54 0.29 0.6 0.360.54 0.29 0.6 0.360.55 0.3 0.6 0.360.55 0.3 0.6 0.360.56 0.31 0.6 0.360.56 0.31 0.6 0.360.57 0.32 0.6 0.360.57 0.32 0.6 0.360.58 0.33 0.6 0.360.58 0.34 0.6 0.360.59 0.34 0.6 0.360.59 0.35 0.6 0.36

0.6 0.35 0.6 0.360.6 0.36 0.7 0.49

0.61 0.37 0.7 0.490.61 0.37 0.7 0.490.62 0.38 0.7 0.490.62 0.38 0.7 0.490.63 0.39 0.7 0.490.63 0.4 0.7 0.490.64 0.4 0.7 0.490.64 0.41 0.7 0.490.65 0.42 0.7 0.490.65 0.42 0.7 0.490.66 0.43 0.7 0.490.66 0.44 0.7 0.490.67 0.44 0.7 0.490.67 0.45 0.7 0.490.68 0.46 0.7 0.49

0.68 0.46 0.7 0.490.69 0.47 0.7 0.490.69 0.48 0.7 0.49

0.7 0.48 0.7 0.490.7 0.49 0.8 0.64

0.71 0.5 0.8 0.640.71 0.5 0.8 0.640.72 0.51 0.8 0.640.72 0.52 0.8 0.64

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0.73 0.53 0.8 0.640.73 0.53 0.8 0.640.74 0.54 0.8 0.640.74 0.55 0.8 0.640.75 0.56 0.8 0.640.75 0.56 0.8 0.64

0.76 0.57 0.8 0.640.76 0.58 0.8 0.640.77 0.59 0.8 0.640.77 0.59 0.8 0.640.78 0.6 0.8 0.640.78 0.61 0.8 0.640.79 0.62 0.8 0.640.79 0.62 0.8 0.64

0.8 0.63 0.8 0.640.8 0.64 0.9 0.81

0.81 0.65 0.9 0.810.81 0.66 0.9 0.810.82 0.66 0.9 0.810.82 0.67 0.9 0.810.83 0.68 0.9 0.810.83 0.69 0.9 0.810.84 0.7 0.9 0.810.84 0.71 0.9 0.810.85 0.71 0.9 0.810.85 0.72 0.9 0.810.86 0.73 0.9 0.810.86 0.74 0.9 0.810.87 0.75 0.9 0.810.87 0.76 0.9 0.810.88 0.77 0.9 0.810.88 0.77 0.9 0.810.89 0.78 0.9 0.810.89 0.79 0.9 0.81

0.9 0.8 0.9 0.810.9 0.81 1 1

0.91 0.82 1 10.91 0.83 1 10.92 0.84 1 10.92 0.85 1 10.93 0.86 1 1

0.93 0.86 1 10.94 0.87 1 10.94 0.88 1 10.95 0.89 1 10.95 0.9 1 10.96 0.91 1 10.96 0.92 1 10.97 0.93 1 10.97 0.94 1 1

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0.98 0.95 1 10.98 0.96 1 10.99 0.97 1 10.99 0.98 1 1

1 0.99 1 11 1 1.1 1.21

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0.1 p q r s0.01 0 0.1 0.01 0.01

1 0.2 0.04 0.042 0.3 0.09 0.093 0.4 0.16 0.164 0.5 0.25 0.255 0.6 0.36 0.366 0.7 0.49 0.497 0.8 0.64 0.648 0.9 0.81 0.819 1 1 1

10 1.1 1.21 0

11 1.2 1.44 0

12 1.3 1.69 013 1.4 1.96 014 1.5 2.25 015 1.6 2.56 016 1.7 2.89 017 1.8 3.24 018 1.9 3.61 019 2 4 020 2.1 4.41 021 2.2 4.84 022 2.3 5.29 0

23 2.4 5.76 0

24 2.5 6.25 025 2.6 6.76 0

26 2.7 7.29 027 2.8 7.84 0

28 2.9 8.41 0

29 3 9 030 3.1 9.61 031 3.2 10.24 032 3.3 10.89 033 3.4 11.56 034 3.5 12.25 035 3.6 12.96 036 3.7 13.69 0

37 3.8 14.44 038 3.9 15.21 039 4 16 040 4.1 16.81 041 4.2 17.64 042 4.3 18.49 043 4.4 19.36 044 4.5 20.25 0

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45 4.6 21.16 046 4.7 22.09 047 4.8 23.04 048 4.9 24.01 049 5 25 050 5.1 26.01 0

51 5.2 27.04 052 5.3 28.09 053 5.4 29.16 054 5.5 30.25 055 5.6 31.36 056 5.7 32.49 057 5.8 33.64 058 5.9 34.81 059 6 36 060 6.1 37.21 061 6.2 38.44 062 6.3 39.69 063 6.4 40.96 064 6.5 42.25 065 6.6 43.56 066 6.7 44.89 067 6.8 46.24 068 6.9 47.61 069 7 49 070 7.1 50.41 071 7.2 51.84 072 7.3 53.29 073 7.4 54.76 074 7.5 56.25 075 7.6 57.76 076 7.7 59.29 077 7.8 60.84 078 7.9 62.41 079 8 64 080 8.1 65.61 081 8.2 67.24 082 8.3 68.89 083 8.4 70.56 084 8.5 72.25 085 8.6 73.96 086 8.7 75.69 087 8.8 77.44 088 8.9 79.21 089 9 81 090 9.1 82.81 091 9.2 84.64 092 9.3 86.49 093 9.4 88.36 094 9.5 90.25 0

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95 9.6 92.16 096 9.7 94.09 097 9.8 96.04 098 9.9 98.01 099 10 100 0

100 10.1 102.01 0

101 10.2 104.04 0102 10.3 106.09 0103 10.4 108.16 0104 10.5 110.25 0105 10.6 112.36 0106 10.7 114.49 0107 10.8 116.64 0108 10.9 118.81 0109 11 121 0110 11.1 123.21 0111 11.2 125.44 0112 11.3 127.69 0113 11.4 129.96 0114 11.5 132.25 0115 11.6 134.56 0116 11.7 136.89 0117 11.8 139.24 0118 11.9 141.61 0119 12 144 0120 12.1 146.41 0121 12.2 148.84 0122 12.3 151.29 0123 12.4 153.76 0124 12.5 156.25 0125 12.6 158.76 0126 12.7 161.29 0127 12.8 163.84 0128 12.9 166.41 0129 13 169 0130 13.1 171.61 0131 13.2 174.24 0132 13.3 176.89 0133 13.4 179.56 0134 13.5 182.25 0135 13.6 184.96 0

136 13.7 187.69 0137 13.8 190.44 0138 13.9 193.21 0139 14 196 0140 14.1 198.81 0141 14.2 201.64 0142 14.3 204.49 0143 14.4 207.36 0144 14.5 210.25 0

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145 14.6 213.16 0146 14.7 216.09 0147 14.8 219.04 0148 14.9 222.01 0149 15 225 0150 15.1 228.01 0

151 15.2 231.04 0152 15.3 234.09 0153 15.4 237.16 0154 15.5 240.25 0155 15.6 243.36 0156 15.7 246.49 0157 15.8 249.64 0158 15.9 252.81 0159 16 256 0160 16.1 259.21 0161 16.2 262.44 0162 16.3 265.69 0163 16.4 268.96 0164 16.5 272.25 0165 16.6 275.56 0166 16.7 278.89 0167 16.8 282.24 0168 16.9 285.61 0169 17 289 0170 17.1 292.41 0171 17.2 295.84 0172 17.3 299.29 0173 17.4 302.76 0174 17.5 306.25 0175 17.6 309.76 0176 17.7 313.29 0177 17.8 316.84 0178 17.9 320.41 0179 18 324 0180 18.1 327.61 0181 18.2 331.24 0182 18.3 334.89 0183 18.4 338.56 0184 18.5 342.25 0185 18.6 345.96 0

186 18.7 349.69 0187 18.8 353.44 0188 18.9 357.21 0189 19 361 0190 19.1 364.81 0191 19.2 368.64 0192 19.3 372.49 0193 19.4 376.36 0194 19.5 380.25 0

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195 19.6 384.16 0196 19.7 388.09 0197 19.8 392.04 0198 19.9 396.01 0199 20 400 0200 20.1 404.01 0

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Important: Macros must be enabled, otherwise the g* This improved and expanded version of the grapher is due to Jeff Morgan, Department of

This worksheet will automatically graph any function of x, show the (middle) Riemann sum a

Instructions: Just enter the function in cell G13 (as shown; no equals sign) enter valuand a value between 1 and 200 for the number of partitions n.

Notes: The number of partitions n cannot exceed 200 for this grapher Function:a:

The graph data is hidden on the right b:

00.03

0.060.09

0.120.15

0.180.21

0.240.27

0.30.33

0.360.39

0.420.45

0.480.51

0.540.57

0.60.63

0.660.69

0.720.75

0.780.81

0.840.87

0.90.93

0.960.99

0

0.2

0.4

0.6

0.8

1

1.2

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Dont touch this table!x y u

0 0 0.05

apher will not work. 0.01 0 0.05athematics, Texas A&M University. 0.01 0 0.05

0.02 0 0.05s a shaded area, and also ita value. 0.02 0 0.05

0.03 0 0.05s for the limits of integration a and b, 0.03 0 0.05

0.04 0 0.050.04 0 0.050.05 0 0.05

x^2 0.05 0 0.050 n: 10 0.06 0 0.051 0.06 0 0.05

0.06 0 0.050.07 0 0.050.08 0.01 0.050.08 0.01 0.050.09 0.01 0.05

Left Sum 0.29 0.09 0.01 0.05Right Sum 0.39 0.1 0.01 0.05

Trapezoid Sum 0.34 0.1 0.01 0.15Midpoint Sum 0.33 0.11 0.01 0.15

Simpson's 0.33 0.11 0.01 0.150.12 0.01 0.150.12 0.01 0.150.13 0.02 0.15

pi 0.13 0.02 0.153.14 0.14 0.02 0.15

e 0.14 0.02 0.152.72 0.15 0.02 0.15

0.15 0.02 0.150.16 0.02 0.150.16 0.03 0.150.17 0.03 0.150.17 0.03 0.150.18 0.03 0.15

0.18 0.03 0.150.19 0.03 0.150.19 0.04 0.15

0.2 0.04 0.150.2 0.04 0.25

0.21 0.04 0.250.21 0.04 0.250.22 0.05 0.250.22 0.05 0.25

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0.23 0.05 0.250.23 0.05 0.250.24 0.06 0.250.24 0.06 0.250.25 0.06 0.250.25 0.06 0.25

0.26 0.07 0.250.26 0.07 0.250.27 0.07 0.250.27 0.07 0.250.28 0.08 0.250.28 0.08 0.250.29 0.08 0.250.29 0.08 0.25

0.3 0.09 0.250.3 0.09 0.35

0.31 0.09 0.350.31 0.1 0.350.32 0.1 0.350.32 0.1 0.350.33 0.11 0.350.33 0.11 0.350.34 0.11 0.350.34 0.12 0.350.35 0.12 0.350.35 0.12 0.350.36 0.13 0.350.36 0.13 0.350.37 0.13 0.350.37 0.14 0.350.38 0.14 0.350.38 0.14 0.350.39 0.15 0.350.39 0.15 0.35

0.4 0.16 0.350.4 0.16 0.45

0.41 0.16 0.450.41 0.17 0.450.42 0.17 0.450.42 0.18 0.450.43 0.18 0.450.43 0.18 0.450.44 0.19 0.450.44 0.19 0.450.45 0.2 0.450.45 0.2 0.450.46 0.21 0.450.46 0.21 0.450.47 0.22 0.450.47 0.22 0.45

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0.48 0.23 0.450.48 0.23 0.450.49 0.24 0.450.49 0.24 0.45

0.5 0.25 0.450.5 0.25 0.55

0.51 0.26 0.550.51 0.26 0.550.52 0.27 0.550.52 0.27 0.550.53 0.28 0.550.53 0.28 0.550.54 0.29 0.550.54 0.29 0.550.55 0.3 0.550.55 0.3 0.550.56 0.31 0.550.56 0.31 0.550.57 0.32 0.550.57 0.32 0.550.58 0.33 0.550.58 0.34 0.550.59 0.34 0.550.59 0.35 0.55

0.6 0.35 0.550.6 0.36 0.65

0.61 0.37 0.650.61 0.37 0.650.62 0.38 0.650.62 0.38 0.650.63 0.39 0.650.63 0.4 0.650.64 0.4 0.650.64 0.41 0.650.65 0.42 0.650.65 0.42 0.650.66 0.43 0.650.66 0.44 0.650.67 0.44 0.650.67 0.45 0.650.68 0.46 0.65

0.68 0.46 0.650.69 0.47 0.650.69 0.48 0.65

0.7 0.48 0.650.7 0.49 0.75

0.71 0.5 0.750.71 0.5 0.750.72 0.51 0.750.72 0.52 0.75

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0.73 0.53 0.750.73 0.53 0.750.74 0.54 0.750.74 0.55 0.750.75 0.56 0.750.75 0.56 0.75

0.76 0.57 0.750.76 0.58 0.750.77 0.59 0.750.77 0.59 0.750.78 0.6 0.750.78 0.61 0.750.79 0.62 0.750.79 0.62 0.75

0.8 0.63 0.750.8 0.64 0.85

0.81 0.65 0.850.81 0.66 0.850.82 0.66 0.850.82 0.67 0.850.83 0.68 0.850.83 0.69 0.850.84 0.7 0.850.84 0.71 0.850.85 0.71 0.850.85 0.72 0.850.86 0.73 0.850.86 0.74 0.850.87 0.75 0.850.87 0.76 0.850.88 0.77 0.850.88 0.77 0.850.89 0.78 0.850.89 0.79 0.85

0.9 0.8 0.850.9 0.81 0.95

0.91 0.82 0.950.91 0.83 0.950.92 0.84 0.950.92 0.85 0.950.93 0.86 0.95

0.93 0.86 0.950.94 0.87 0.950.94 0.88 0.950.95 0.89 0.950.95 0.9 0.950.96 0.91 0.950.96 0.92 0.950.97 0.93 0.950.97 0.94 0.95

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0.98 0.95 0.950.98 0.96 0.950.99 0.97 0.950.99 0.98 0.95

1 0.99 0.951 1 1.05

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y_u 0.1 p q r s t u0 0.01 0 0.05 0 0 0 0

0 1 0.15 0.02 0.02 0.1 0.010 2 0.25 0.06 0.06 0.2 0.040 3 0.35 0.12 0.12 0.3 0.090 4 0.45 0.2 0.2 0.4 0.160 5 0.55 0.3 0.3 0.5 0.250 6 0.65 0.42 0.42 0.6 0.360 7 0.75 0.56 0.56 0.7 0.490 8 0.85 0.72 0.72 0.8 0.640 9 0.95 0.9 0.9 0.9 0.81

0 10 1.05 1.1 0 1 1

0 11 1.15 1.32 0 1.1 1.21

0 12 1.25 1.56 0 1.2 1.440 13 1.35 1.82 0 1.3 1.690 14 1.45 2.1 0 1.4 1.960 15 1.55 2.4 0 1.5 2.250 16 1.65 2.72 0 1.6 2.560 17 1.75 3.06 0 1.7 2.89

0 18 1.85 3.42 0 1.8 3.24

0 19 1.95 3.8 0 1.9 3.61

0.02 20 2.05 4.2 0 2 4

0.02 21 2.15 4.62 0 2.1 4.41

0.02 22 2.25 5.06 0 2.2 4.840.02 23 2.35 5.52 0 2.3 5.290.02 24 2.45 6 0 2.4 5.760.02 25 2.55 6.5 0 2.5 6.25

0.02 26 2.65 7.02 0 2.6 6.76

0.02 27 2.75 7.56 0 2.7 7.29

0.02 28 2.85 8.12 0 2.8 7.84

0.02 29 2.95 8.7 0 2.9 8.410.02 30 3.05 9.3 0 3 90.02 31 3.15 9.92 0 3.1 9.610.02 32 3.25 10.56 0 3.2 10.240.02 33 3.35 11.22 0 3.3 10.890.02 34 3.45 11.9 0 3.4 11.560.02 35 3.55 12.6 0 3.5 12.25

0.02 36 3.65 13.32 0 3.6 12.960.02 37 3.75 14.06 0 3.7 13.690.02 38 3.85 14.82 0 3.8 14.440.02 39 3.95 15.6 0 3.9 15.210.06 40 4.05 16.4 0 4 160.06 41 4.15 17.22 0 4.1 16.810.06 42 4.25 18.06 0 4.2 17.640.06 43 4.35 18.92 0 4.3 18.490.06 44 4.45 19.8 0 4.4 19.36

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0.06 45 4.55 20.7 0 4.5 20.250.06 46 4.65 21.62 0 4.6 21.160.06 47 4.75 22.56 0 4.7 22.090.06 48 4.85 23.52 0 4.8 23.040.06 49 4.95 24.5 0 4.9 24.010.06 50 5.05 25.5 0 5 25

0.06 51 5.15 26.52 0 5.1 26.010.06 52 5.25 27.56 0 5.2 27.040.06 53 5.35 28.62 0 5.3 28.090.06 54 5.45 29.7 0 5.4 29.160.06 55 5.55 30.8 0 5.5 30.250.06 56 5.65 31.92 0 5.6 31.360.06 57 5.75 33.06 0 5.7 32.490.06 58 5.85 34.22 0 5.8 33.640.06 59 5.95 35.4 0 5.9 34.810.12 60 6.05 36.6 0 6 360.12 61 6.15 37.82 0 6.1 37.210.12 62 6.25 39.06 0 6.2 38.440.12 63 6.35 40.32 0 6.3 39.690.12 64 6.45 41.6 0 6.4 40.960.12 65 6.55 42.9 0 6.5 42.250.12 66 6.65 44.22 0 6.6 43.560.12 67 6.75 45.56 0 6.7 44.890.12 68 6.85 46.92 0 6.8 46.240.12 69 6.95 48.3 0 6.9 47.610.12 70 7.05 49.7 0 7 490.12 71 7.15 51.12 0 7.1 50.410.12 72 7.25 52.56 0 7.2 51.840.12 73 7.35 54.02 0 7.3 53.290.12 74 7.45 55.5 0 7.4 54.760.12 75 7.55 57 0 7.5 56.250.12 76 7.65 58.52 0 7.6 57.760.12 77 7.75 60.06 0 7.7 59.290.12 78 7.85 61.62 0 7.8 60.840.12 79 7.95 63.2 0 7.9 62.41

0.2 80 8.05 64.8 0 8 640.2 81 8.15 66.42 0 8.1 65.610.2 82 8.25 68.06 0 8.2 67.240.2 83 8.35 69.72 0 8.3 68.890.2 84 8.45 71.4 0 8.4 70.560.2 85 8.55 73.1 0 8.5 72.250.2 86 8.65 74.82 0 8.6 73.960.2 87 8.75 76.56 0 8.7 75.690.2 88 8.85 78.32 0 8.8 77.440.2 89 8.95 80.1 0 8.9 79.210.2 90 9.05 81.9 0 9 810.2 91 9.15 83.72 0 9.1 82.810.2 92 9.25 85.56 0 9.2 84.640.2 93 9.35 87.42 0 9.3 86.490.2 94 9.45 89.3 0 9.4 88.36

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0.2 95 9.55 91.2 0 9.5 90.250.2 96 9.65 93.12 0 9.6 92.160.2 97 9.75 95.06 0 9.7 94.090.2 98 9.85 97.02 0 9.8 96.040.2 99 9.95 99 0 9.9 98.010.3 100 10.05 101 0 10 100

0.3 101 10.15 103.02 0 10.1 102.010.3 102 10.25 105.06 0 10.2 104.040.3 103 10.35 107.12 0 10.3 106.090.3 104 10.45 109.2 0 10.4 108.160.3 105 10.55 111.3 0 10.5 110.250.3 106 10.65 113.42 0 10.6 112.360.3 107 10.75 115.56 0 10.7 114.490.3 108 10.85 117.72 0 10.8 116.640.3 109 10.95 119.9 0 10.9 118.810.3 110 11.05 122.1 0 11 1210.3 111 11.15 124.32 0 11.1 123.210.3 112 11.25 126.56 0 11.2 125.440.3 113 11.35 128.82 0 11.3 127.690.3 114 11.45 131.1 0 11.4 129.960.3 115 11.55 133.4 0 11.5 132.250.3 116 11.65 135.72 0 11.6 134.560.3 117 11.75 138.06 0 11.7 136.890.3 118 11.85 140.42 0 11.8 139.240.3 119 11.95 142.8 0 11.9 141.61

0.42 120 12.05 145.2 0 12 1440.42 121 12.15 147.62 0 12.1 146.410.42 122 12.25 150.06 0 12.2 148.840.42 123 12.35 152.52 0 12.3 151.290.42 124 12.45 155 0 12.4 153.760.42 125 12.55 157.5 0 12.5 156.250.42 126 12.65 160.02 0 12.6 158.760.42 127 12.75 162.56 0 12.7 161.290.42 128 12.85 165.12 0 12.8 163.840.42 129 12.95 167.7 0 12.9 166.410.42 130 13.05 170.3 0 13 1690.42 131 13.15 172.92 0 13.1 171.610.42 132 13.25 175.56 0 13.2 174.240.42 133 13.35 178.22 0 13.3 176.890.42 134 13.45 180.9 0 13.4 179.560.42 135 13.55 183.6 0 13.5 182.25

0.42 136 13.65 186.32 0 13.6 184.960.42 137 13.75 189.06 0 13.7 187.690.42 138 13.85 191.82 0 13.8 190.440.42 139 13.95 194.6 0 13.9 193.210.56 140 14.05 197.4 0 14 1960.56 141 14.15 200.22 0 14.1 198.810.56 142 14.25 203.06 0 14.2 201.640.56 143 14.35 205.92 0 14.3 204.490.56 144 14.45 208.8 0 14.4 207.36

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0.56 145 14.55 211.7 0 14.5 210.250.56 146 14.65 214.62 0 14.6 213.160.56 147 14.75 217.56 0 14.7 216.090.56 148 14.85 220.52 0 14.8 219.040.56 149 14.95 223.5 0 14.9 222.010.56 150 15.05 226.5 0 15 225

0.56 151 15.15 229.52 0 15.1 228.010.56 152 15.25 232.56 0 15.2 231.040.56 153 15.35 235.62 0 15.3 234.090.56 154 15.45 238.7 0 15.4 237.160.56 155 15.55 241.8 0 15.5 240.250.56 156 15.65 244.92 0 15.6 243.360.56 157 15.75 248.06 0 15.7 246.490.56 158 15.85 251.22 0 15.8 249.640.56 159 15.95 254.4 0 15.9 252.810.72 160 16.05 257.6 0 16 2560.72 161 16.15 260.82 0 16.1 259.210.72 162 16.25 264.06 0 16.2 262.440.72 163 16.35 267.32 0 16.3 265.690.72 164 16.45 270.6 0 16.4 268.960.72 165 16.55 273.9 0 16.5 272.250.72 166 16.65 277.22 0 16.6 275.560.72 167 16.75 280.56 0 16.7 278.890.72 168 16.85 283.92 0 16.8 282.240.72 169 16.95 287.3 0 16.9 285.610.72 170 17.05 290.7 0 17 2890.72 171 17.15 294.12 0 17.1 292.410.72 172 17.25 297.56 0 17.2 295.840.72 173 17.35 301.02 0 17.3 299.290.72 174 17.45 304.5 0 17.4 302.760.72 175 17.55 308 0 17.5 306.250.72 176 17.65 311.52 0 17.6 309.760.72 177 17.75 315.06 0 17.7 313.290.72 178 17.85 318.62 0 17.8 316.840.72 179 17.95 322.2 0 17.9 320.41

0.9 180 18.05 325.8 0 18 3240.9 181 18.15 329.42 0 18.1 327.610.9 182 18.25 333.06 0 18.2 331.240.9 183 18.35 336.72 0 18.3 334.890.9 184 18.45 340.4 0 18.4 338.560.9 185 18.55 344.1 0 18.5 342.25

0.9 186 18.65 347.82 0 18.6 345.960.9 187 18.75 351.56 0 18.7 349.690.9 188 18.85 355.32 0 18.8 353.440.9 189 18.95 359.1 0 18.9 357.210.9 190 19.05 362.9 0 19 3610.9 191 19.15 366.72 0 19.1 364.810.9 192 19.25 370.56 0 19.2 368.640.9 193 19.35 374.42 0 19.3 372.490.9 194 19.45 378.3 0 19.4 376.36

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0.9 195 19.55 382.2 0 19.5 380.250.9 196 19.65 386.12 0 19.6 384.160.9 197 19.75 390.06 0 19.7 388.090.9 198 19.85 394.02 0 19.8 392.040.9 199 19.95 398 0 19.9 396.011.1 200 20.05 402 0 20 400

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left right0 0

0.01 0.010.04 0.040.09 0.090.16 0.160.25 0.250.36 0.360.49 0.490.64 0.640.81 0.81

0 1

0 0

0 00 00 00 00 00 0

0 0

0 0

0 0

0 0

0 00 00 00 0

0 0

0 0

0 0

0 00 00 00 00 00 00 0

0 00 00 00 00 00 00 00 00 0

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0 00 00 00 00 00 0

0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0

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0 00 00 00 00 00 0

0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0

0 00 00 00 00 00 00 00 00 0

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0 00 00 00 00 00 0

0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0

0 00 00 00 00 00 00 00 00 0

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0 00 00 00 00 00 0