Areas and Distances Integration

Simpson’s rule assumes that boundary between the ordinates are parabolic arcs.

• True

• False

Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.

• 116.88 sq. m

• 161.88 sq. m

• 611.88 sq. m

• 169.54 sq. m

Among the area calculation methods, which is more accurate?

• Area by co-ordinates

• Area by Simpson’s rule

• Area by trapezoidal rule

• Area by offsets

Which of the following indicates the formula for Simpson’s rule?

• Δ = (d/3)*((O₀+O_n) + 4*(O₁+O₃+……..) + 2*(O₂+O₄+……….))

• Δ = (d/3)*((O₀+O_n) + 2*(O₁+O₃+……..) + 2*(O₂+O₄+……….))

• Δ = (d/3)*((O₀+O_n) + 4*(O₁+O₃+……..) + 2*(O₂+O₄+……….))

• Δ = (d/3)*((O₀+O_n) + 2*(O₁+O₃+……..) + 4*(O₂+O₄+……….))

Use the function values in the following table and the Trapezoidal Rule with n=6 to approximate the integral from x=0 to x=6.
x:     0     1     2     3      4     5     6  
f(x): 12   10    9    11    13   16    18

• 71
• 74
• 77
• 89

Use the function values in the following table and the Trapezoidal Rule with n=6 to approximate the integral from x=0 to x=12.
x:     0     2     4     6      8    10    12  
f(x):  7   11    20   25    18   14     9

• 96
• 102
• 190
• 192

Use the function values in the following table and the Trapezoidal Rule with n=5 to approximate the integral from x=0 to x=8.
x:     0     2     5     7      8            
f(x):  6    13   20   22    25

• 134
• 141
• 268
• 282

Use the function values in the following table and RRAM to approximate the integral from x=0 to x=6.
x:      0     1     2     3      4     5      6  
f(x): 12   10    9    11    13   16    18

• 71
• 74
• 77
• 78

Use the function values in the following table and LRAM to approximate the integral from x=0 to x=6.
x:      0     1     2     3      4     5      6  
f(x): 12   10    9    11    13   16    18

• 71
• 74
• 77
• 78

Use the function values in the following table and MRAM with n=3 to approximate the integral from x=0 to x=12.
x:     0     2     4     6      8    10    12  
f(x):  7   11    20   25    18   14     9

• 100
• 200
• 300
• 400