Integration or Riemann Sums: Which is More Effective for Numerical Integration?

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Homework Help Overview

The discussion revolves around the effectiveness of Riemann sums compared to direct integration for numerical integration, exploring their educational purpose and practical applications.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore whether Riemann sums have practical advantages over integration, with some suggesting they are primarily educational tools. Others discuss their role in understanding integration and proofs.

Discussion Status

The conversation is ongoing, with various perspectives on the utility of Riemann sums being presented. Some participants affirm the educational value of Riemann sums while others question their practicality in complex scenarios.

Contextual Notes

There is an implicit assumption that Riemann sums are foundational for understanding integration, but the discussion also highlights potential limitations in their application to complex functions.

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Is there ever a situation where it is more appropriate/advantageous to use Riemann summation as opposed to evaluating an integral, or is Riemann summation merely taught in order to help the student to understand what's going on?
 
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I always thought the Riemann sum was more fun to do!
 
I would say that Riemann sums are taught primarily for grasping the concept of integration. It becomes impractical/impossible for complex functions and I can't think of a time when it would be easier.
 
Riemann sums are not "merely" taught to "understand what is going on".
They are taught because the PROOFS of Riemann integration depend on them, and as it happens, it is proofs that constitute the soul of maths, not nifty calculation techniques.
 
Last edited:
Thats true.
 
Numerical integration techniques are based on Riemann sums.

Also, typically the way one sets up an integral in a particular application is typically based on the Riemann sum concept.
 

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