Visualizing Simpson's Rule: Area Under the Curve

  • Context: Undergrad 
  • Thread starter Thread starter JNeutron2186
  • Start date Start date
  • Tags Tags
    Area Curve
Click For Summary

Discussion Overview

The discussion revolves around visualizing Simpson's Rule, particularly in comparison to Riemann sums which use rectangles and trapezoids for approximating the area under a curve. Participants explore how to represent this theorem visually and conceptually.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant inquires about visual representations of Simpson's Rule, similar to those used for Riemann sums.
  • Another participant explains that Simpson's Rule approximates the function graph using a parabola through three consecutive points, contrasting it with the trapezoid rule.
  • A link to a Wikipedia page on Simpson's Rule is shared for further reference.

Areas of Agreement / Disagreement

Participants do not appear to have reached a consensus on the best visual representation, and the discussion remains open to further exploration.

Contextual Notes

There may be limitations in the visual representation of the theorem, as well as assumptions about the familiarity with the concepts of Riemann sums and trapezoidal approximations.

JNeutron2186
Messages
7
Reaction score
0
Is there a visual way to represent this theorem? Like Riemanns rules with rectangles and trapezoids? I know the clear cut way to evaluate the area under the curve using the rule on a closed set. Soooo any thoughts?CORRECTION THIS IS SIMPSONS RULE*typo...
 
Physics news on Phys.org
Just as the trapezoid rule approximates the function graph by straight lines between two consecutive points, Simpson's rule approximates the function graph by a parabola through three consecutive points.
 
Thanks!
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 24 ·
Replies
24
Views
4K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K