Trapezoidal Approximation Error

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SUMMARY

The discussion centers on the trapezoidal approximation error in numerical integration, specifically addressing the conditions for achieving two decimal place accuracy. The consensus is that using N = 20 intervals is appropriate, and the error should be expressed as less than 0.005 to ensure the desired accuracy. Participants clarified the use of the inequality, favoring "<" over "≤" for error estimation.

PREREQUISITES
  • Understanding of numerical integration techniques
  • Familiarity with the trapezoidal rule
  • Knowledge of error analysis in numerical methods
  • Basic mathematical concepts of inequalities
NEXT STEPS
  • Study the trapezoidal rule in detail, focusing on its derivation and applications
  • Learn about error bounds in numerical integration
  • Explore other numerical methods for integration, such as Simpson's rule
  • Investigate the impact of interval selection on accuracy in numerical methods
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Students in mathematics or engineering courses, educators teaching numerical analysis, and professionals involved in computational methods requiring precise integration techniques.

theBEAST
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Homework Statement


qFkVv.png


The Attempt at a Solution


rdqgf.jpg

Thus my answer is N = 20.

I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?
 
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theBEAST said:

Homework Statement


qFkVv.png


The Attempt at a Solution


rdqgf.jpg

Thus my answer is N = 20.

I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?

Your work looks fine to me, but I think I would use < instead of ≤. If your error < .005, you'll be guaranteed 2 decimal place accuracy.
 

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