Understanding the basics of integration

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Discussion Overview

The discussion revolves around the understanding of integration in calculus, specifically focusing on the concept of partitioning the area under a curve and the relationship between lower and upper sums. The context includes learning resources and explanations related to these concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Homework-related

Main Points Raised

  • One participant reflects on their understanding of integrals as the limit of lower and upper sums approaching the same value as the number of partitions increases.
  • Another participant acknowledges the understanding and questions what further explanation is needed.
  • A suggestion is made to explore variations of explanations by researching terms like 'Riemann sum' and 'fundamental theorem of calculus'.
  • A similar acknowledgment of understanding is reiterated, expressing gratitude for the support received.

Areas of Agreement / Disagreement

Participants generally agree on the understanding of the concept presented, but there is no explicit consensus on what further clarification is needed.

Contextual Notes

Some assumptions about prior knowledge of calculus concepts may not be explicitly stated, and the discussion does not resolve any potential misunderstandings about the definitions involved.

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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