Understanding the basics of integration

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SUMMARY

The discussion centers on the understanding of integration, specifically through the lens of Riemann sums as introduced in Spivak's calculus book. Participants confirm that as the number of partitions increases, the lower and upper sums converge to the same value, representing the area under the curve. This convergence is a fundamental concept in calculus, illustrating the definition of the integral. The conversation encourages further exploration of related concepts for deeper comprehension.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with Riemann sums
  • Knowledge of the fundamental theorem of calculus
  • Ability to interpret graphical representations of functions
NEXT STEPS
  • Research Riemann sums in detail
  • Study the fundamental theorem of calculus
  • Explore graphical methods for visualizing integrals
  • Practice problems involving partitioning areas under curves
USEFUL FOR

Students learning calculus, educators teaching integration concepts, and anyone seeking to deepen their understanding of mathematical analysis.

Mohankpvk
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I tried learning calculus using the book by Spivak.In this text, while introducing integrals the author explained a lot about partitioning the area under the curve and defined the integral.The way I understood this is, as we increase the number of divisions in the partition the lower sum and the the up sum approach the same value and this value is the area under the curve.Am I understanding it right? Please explain.
 
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You are doing fine. 'Please explain' is a strange request: what exactly would you like explained on top of that explanation :biggrin: ?
 
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Sometimes it helps to study variations of the same explanation. Google 'Riemann sum' or 'fundamental theorem of calculus' to find lots of those.
 
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BvU said:
You are doing fine. 'Please explain' is a strange request: what exactly would you like explained on top of that explanation [emoji3] ?
Thank you.That meant a lot to me.
 

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