Trouble converting definite integrals to Riemann's and back

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SUMMARY

The discussion focuses on the conversion of definite integrals to Riemann sums and vice versa, specifically addressing the integral \(\int_0^1 f(x)dx\) and its approximation using the Riemann sum \(\frac{1}{n}\sum_{k=1}^n f\left(\frac{k-1/2}{n}\right)\). Participants seek clear, step-by-step explanations of this process, emphasizing the importance of understanding the role of large \(n\) in simplifying the expression by ignoring the \(-1/2\) term. The conversation highlights the need for clarity in mathematical communication, particularly for those struggling with foundational concepts.

PREREQUISITES
  • Understanding of definite integrals
  • Familiarity with Riemann sums
  • Basic knowledge of limits and convergence
  • Proficiency in mathematical notation and expressions
NEXT STEPS
  • Study the properties of definite integrals in calculus
  • Learn about the derivation and application of Riemann sums
  • Explore the concept of limits in the context of integration
  • Review examples of converting between integrals and Riemann sums
USEFUL FOR

Students of calculus, mathematics educators, and anyone seeking to deepen their understanding of integration techniques and Riemann sums.

Terrell
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can i request anyone to please show me the step by step with specific explanations? thank you! i saw this on stackexchange, and the steps shown are really fuzzy to me :(
 

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Physics news on Phys.org
In general [itex]\int_0^1 f(x)dx[/itex] can be approximated by a Riemann sum [itex]\frac{1}{n}\sum_{k=1}^n f(\frac{k-1/2}{n})[/itex]. For large n, -1/2 can be ignored.
 

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