dx 0.1 Integral between

x-axis Functionerivative Rectangles Integral-5 -36 -3.6 -3.6

-4.9 -28.438 75.620 -2.844 -6.444-4.8 -21.344 70.940 -2.134 -8.578-4.7 -14.706 66.380 -1.471 -10.049-4.6 -8.512 61.940 -0.851 -10.900-4.5 -2.750 57.620 -0.275 -11.175-4.4 2.592 53.420 0.259 -10.916-4.3 7.526 49.340 0.753 -10.163-4.2 12.064 45.380 1.206 -8.957-4.1 16.218 41.540 1.622 -7.335-4 20.000 37.820 2.000 -5.335

-3.9 23.422 34.220 2.342 -2.993-3.8 26.496 30.740 2.650 -0.343-3.7 29.234 27.380 2.923 2.580-3.6 31.648 24.140 3.165 5.745-3.5 33.750 21.020 3.375 9.120-3.4 35.552 18.020 3.555 12.675-3.3 37.066 15.140 3.707 16.382-3.2 38.304 12.380 3.830 20.212-3.1 39.278 9.740 3.928 24.140-3 40.000 7.220 4.000 28.140

-2.9 40.482 4.820 4.048 32.188-2.8 40.736 2.540 4.074 36.262-2.7 40.774 0.380 4.077 40.339-2.6 40.608 -1.660 4.061 44.400-2.5 40.250 -3.580 4.025 48.425-2.4 39.712 -5.380 3.971 52.396-2.3 39.006 -7.060 3.901 56.297-2.2 38.144 -8.620 3.814 60.111-2.1 37.138 -10.060 3.714 63.825-2 36.000 -11.380 3.600 67.425

-1.9 34.742 -12.580 3.474 70.899-1.8 33.376 -13.660 3.338 74.237-1.7 31.914 -14.620 3.191 77.428-1.6 30.368 -15.460 3.037 80.465-1.5 28.750 -16.180 2.875 83.340-1.4 27.072 -16.780 2.707 86.047-1.3 25.346 -17.260 2.535 88.582-1.2 23.584 -17.620 2.358 90.940-1.1 21.798 -17.860 2.180 93.120-1 20.000 -17.980 2.000 95.120

-0.9 18.202 -17.980 1.820 96.940-0.8 16.416 -17.860 1.642 98.582

-6 -4 -2 0 2 4 6

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Function and Derivative of x

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First derivative(x)

Integral from first value(x)

Using Excel for calculus: derivatives and integration

-0.7 14.654 -17.620 1.465 100.047-0.6 12.928 -17.260 1.293 101.340-0.5 11.250 -16.780 1.125 102.465-0.4 9.632 -16.180 0.963 103.428-0.3 8.086 -15.460 0.809 104.237-0.2 6.624 -14.620 0.662 104.899-0.1 5.258 -13.660 0.526 105.425

-1.027E-15 4.000 -12.580 0.400 105.8250.1 2.862 -11.380 0.286 106.1110.2 1.856 -10.060 0.186 106.2970.3 0.994 -8.620 0.099 106.3960.4 0.288 -7.060 0.029 106.4250.5 -0.250 -5.380 -0.025 106.4000.6 -0.608 -3.580 -0.061 106.3390.7 -0.774 -1.660 -0.077 106.2620.8 -0.736 0.380 -0.074 106.1880.9 -0.482 2.540 -0.048 106.1401 0.000 4.820 0.000 106.140

1.1 0.722 7.220 0.072 106.2121.2 1.696 9.740 0.170 106.3821.3 2.934 12.380 0.293 106.6751.4 4.448 15.140 0.445 107.1201.5 6.250 18.020 0.625 107.7451.6 8.352 21.020 0.835 108.5801.7 10.766 24.140 1.077 109.6571.8 13.504 27.380 1.350 111.0071.9 16.578 30.740 1.658 112.6652 20.000 34.220 2.000 114.665

2.1 23.782 37.820 2.378 117.0432.2 27.936 41.540 2.794 119.8372.3 32.474 45.380 3.247 123.0842.4 37.408 49.340 3.741 126.8252.5 42.750 53.420 4.275 131.1002.6 48.512 57.620 4.851 135.9512.7 54.706 61.940 5.471 141.4222.8 61.344 66.380 6.134 147.5562.9 68.438 70.940 6.844 154.4003 76.000 75.620 7.600 162.000

3.1 84.042 80.420 8.404 170.4043.2 92.576 85.340 9.258 179.6623.3 101.614 90.380 10.161 189.8233.4 111.168 95.540 11.117 200.9403.5 121.250 100.820 12.125 213.0653.6 131.872 106.220 13.187 226.2523.7 143.046 111.740 14.305 240.5573.8 154.784 117.380 15.478 256.0353.9 167.098 123.140 16.710 272.7454 180.000 129.020 18.000 290.745

4.1 193.502 135.020 19.350 310.0954.2 207.616 141.140 20.762 330.857

4.3 222.354 147.380 22.235 353.0924.4 237.728 153.740 23.773 376.8654.5 253.750 160.220 25.375 402.2404.6 270.432 166.820 27.043 429.2834.7 287.786 173.540 28.779 458.0624.8 305.824 180.380 30.582 488.6444.9 324.558 187.340 32.456 521.1005 344.000 194.420 34.400 555.500

-2 and 3 is 94.575

-6 -4 -2 0 2 4 6

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100

200

300

400

500

600

Function and Derivative of x

f(x)

First derivative(x)

Integral from first value(x)

Using Excel for calculus: derivatives and integration