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Riemann Sum Homework Review. Pg. 505 # 7-10. n = 8. 1.00 1.02 1.06 1.12 1.19 1.27 1.34 1.42 1.50. X 0 = 0 X 1 = X 2 = X 3 = X 4 = X 5 = X 6 = X 7 = X 8 = 2. Y 0 = Y 1 = Y 2 = Y 3 = Y 4 = Y 5 = Y 6 = Y 7 = Y 8 =. 0.25 0.5 0.75 1 1.25 1.5 1.75. - PowerPoint PPT Presentation
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Riemann Sum Homework Review
Pg. 505 # 7-10
X0 = 0X1 =X2 =X3 =X4 =X5 =X6 =X7 =X8 = 2
n = 8
0.250.50.7511.251.51.75
Y0 = Y1 =Y2 =Y3 =Y4 =Y5 =Y6 =Y7 =Y8 =
1.001.021.061.121.191.271.341.421.50
LHS = 0.25 * 9.41 = 2.35
RHS = 0.25 * 9.90 = 2.48
X0 = 0X1 =X2 =X3 =X4 =X5 =X6 =X7 =X8 = 2
n = 8
0.250.50.7511.251.51.75
Y0 = Y1 =Y2 =Y3 =Y4 =Y5 =Y6 =Y7 =Y8 =
1.001.021.061.121.191.271.341.421.50
* 0.5 = 0.50* 1 = 1.02* 1 = 1.06* 1 = 1.12* 1 = 1.19* 1 = 1.27* 1 = 1.34* 1 = 1.42* 0.5 = 0.75
9.66 * 0.25 = 2.41 Trap.
X0 = 0X1 =X2 =X3 =X4 =X5 =X6 =X7 =X8 = 2
n = 8
0.250.50.7511.251.51.75
X0.5 = 0.125X1.5 = 0.375X2.5 = 0.625X3.5 = 0.875X4.5 = 1.135X5.5 = 1.375X6.5 = 1.625X7.5 = 1.875
Y0.5 = 1.00Y1.5 = 1.03Y2.5 = 1.09Y3.5 = 1.15Y4.5 = 1.23Y5.5 = 1.30Y6.5 = 1.38Y7.5 = 1.469.65 * 0.25 = 2.41 Midpt.
X0 = 0X1 =X2 =X3 =X4 = 0.5
n = 4
0.1250.250.375
Y0 = Y1 =Y2 =Y3 =Y4 =
0.000.020.060.140.25
LHS = 0.218 * 0.125 = 0.027
RHS = 0.466 * 0.125 = 0.058
X0 = 0X1 =X2 =X3 =X4 = 0.5
n = 4
0.1250.250.375
Y0 = Y1 =Y2 =Y3 =Y4 =
0.000.020.060.140.25
* 0.5 = 0.00* 1 = 0.02* 1 = 0.06* 1 = 0.14* 0.5 = 0.12
0.342 * 0.125 = 0.043
Trap.
X0 = 0X1 =X2 =X3 =X4 = 0.5
n = 4
0.1250.250.375
X0.5 = 0.0625X1.5 = 0.1875X2.5 = 0.3125X3.5 = 0.4375
Y0.5 = 0.00Y1.5 = 0.04Y2.5 = 0.10Y3.5 = 0.19
0.327 * 0.125 = 0.041
Midpt.
X0 = 1X1 =X2 =X3 =X4 =X5 =X6 =X7 =X8 = X9 = X10 = 2
n = 10
1.11.21.31.41.51.61.71.81.9
Y0 = Y1 =Y2 =Y3 =Y4 =Y5 =Y6 =Y7 =Y8 = Y9 = Y10 =
0.000.050.080.110.140.160.180.200.210.220.23
LHS = 1.35 * 0.1 = 0.135
RHS = 1.58 * 0.1 = 0.158
X0 = 1X1 =X2 =X3 =X4 =X5 =X6 =X7 =X8 = X9 = X10 = 2
1.11.21.31.41.51.61.71.81.9
Y0 = Y1 =Y2 =Y3 =Y4 =Y5 =Y6 =Y7 =Y8 =Y9 = Y10 =
0.000.050.080.110.140.160.180.200.210.220.23
* 0.5 = 0.00* 1 = 0.05* 1 = 0.08* 1 = 0.11* 1 = 0.14* 1 = 0.16* 1 = 0.17* 1 = 0.20* 1 = 0.21* 1 = 0.22* 0.5 = 0.12
Trapezoidal Rule1.47 * 0.1 = 0.147
n = 10
X0 = 1X1 =X2 =X3 =X4 =X5 =X6 =X7 =X8 = X8 = X8 = 2
1.11.21.31.41.51.61.71.81.9
X0.5 = 1.05X1.5 = 1.15X2.5 = 1.25X3.5 = 1.35X4.5 = 1.45X5.5 = 1.55X6.5 = 1.65X7.5 = 1.75X8.5 = 1.85X9.5 = 1.95
Y0.5 = 0.02Y1.5 = 0.07Y2.5 = 0.10Y3.5 = 0.13Y4.5 = 0.15Y5.5 = 0.17Y6.5 = 0.19Y7.5 = 0.20X8.5 = 0.22X9.5 = 0.23
n = 10
Midpoint Rule1.47 * 0.1 = 0.147
X0 = 0X1 =X2 =X3 =X4 =X5 =X6 = 3
n = 6
0.511.522.5
Y0 = Y1 =Y2 =Y3 =Y4 =Y5 =Y6 =
1.000.760.330.120.050.020.01
LHS = 2.28 * 0.5 = 1.14
RHS = 1.30 * 0.5 = 0.65
X0 = 0X1 =X2 =X3 =X4 =X5 =X6 = 3
0.511.522.5
Y0 = Y1 =Y2 =Y3 =Y4 =Y5 =Y6 =
1.000.760.330.120.050.020.01
* 0.5 = 0.50* 1 = 0.76* 1 = 0.33* 1 = 0.12* 1 = 0.05* 1 = 0.02* 0.5 = 0.005
1.79 * 0.5 = 0.90 Trap.
n = 6
X0 = 0X1 =X2 =X3 =X4 =X5 =X6 = 3
0.511.522.5
X0.5 = 0.25X1.5 = 0.75X2.5 = 1.25X3.5 = 1.75X4.5 = 2.25X5.5 = 2.75
Y0.5 = 0.94Y1.5 = 0.53Y2.5 = 0.20Y3.5 = 0.07Y4.5 = 0.03Y5.5 = 0.02
1.79 * 0.5 = 0.90 Midpt.
n = 6
