Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

MOOC | MOBILE | VIDEOS | BLOG | YOUTUBE | TWITTER | COMMENTS | ANALYTICS | ABOUT | CONTACT | COURSE WEBSITES | BOOKS | MATH FOR COLLEGE


 

MULTIPLE CHOICE TEST

(All Tests)

ROMBERG METHOD

(More on Romberg Method)

INTEGRATION

(More on Integration)

 

Pick the most appropriate answer

 


If  is the value of integral  using n-segment Trapezoidal rule, a better estimate of the integral can be found using Richardsonís 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

 

t(s)

2

4

6

8

10

25

0.166

0.55115

1.8299

6.0755

20.172

8137.5

 

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


 

Complete Solution

 

Multiple choice questions on other topics


AUDIENCE |  AWARDS  |  PEOPLE  |  TRACKS  |  DISSEMINATION  |  PUBLICATIONS


Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

ANALYTICS