If  is the value of integral  using n-segment Trapezoidal rule, a better estimate of the integral can be found using Richardson’s extrapolation as

The estimate of an integral of  is given as 1860.9 using 1-segment Trapezoidal rule. 

Given f(7)=20.27, f(11)=45.125, and f(14)=82.23, the value of the integral using 2-segment Trapezoidal rule would most nearly be

787.32

1072.0

1144.9

1291.5

The value of an integral given using 1, 2, and 4 segments Trapezoidal rule is given as 5.3460, 2.7708, and 1.7536, respectively.  The best estimate of the integral you can find using Romberg integration is most nearly

1.3355
1.3813

1.4145
1.9124

Without using the formula for one-segment Trapezoidal rule for estimating the true error,  can be found directly as well as exactly by using the formula

 ,

For , the true error, in one-segment Trapezoidal rule is given by

 , . 

The value offor the integral  is most nearly

2.7998

4.8500

4.9601

5.0327

Given the velocity vs. time data for a body

The best estimate for distance covered between 2s and 10s by using Romberg rule based on Trapezoidal rule results would be

33.456 m

36.877 m

37.251 m

81.350 m

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