What Is the Correct Approach to Find the Centroid of a Parabolic Area?

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SUMMARY

The correct approach to find the centroid of a parabolic area involves setting up the integral accurately. The user struggled with the centroid calculation for the area defined by the curve y = x^2, specifically obtaining the x centroid as (3/8)b. The integral setup was identified as a potential issue, particularly the expression for dA, which should be defined as dA = h - y dx. The relationship between the curve's parameters (b, h) is crucial for solving the problem correctly.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with the concept of centroids in geometry.
  • Knowledge of parabolic equations and their properties.
  • Experience with setting up area integrals for two-dimensional shapes.
NEXT STEPS
  • Study the derivation of centroids for various geometric shapes.
  • Learn about the application of integration in finding areas under curves.
  • Explore advanced calculus topics related to double integrals and their applications.
  • Review examples of centroid calculations for different polynomial curves.
USEFUL FOR

Students in calculus courses, geometry enthusiasts, and anyone involved in engineering or physics requiring knowledge of centroid calculations for parabolic areas.

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[SOLVED] Centroid Parabolic area

Homework Statement


http://img227.imageshack.us/img227/7518/slowge9.th.jpg
Find the centroid of the area.

Homework Equations


The Attempt at a Solution



I'm not quite sure what I'm screwing up on this problem, I can do other problems like when y = x^2. I have only shown my work for the x centroid, but I can't seem to get the answer (3/8b). Does anyone see where I messed up, I assume it's somewhere in the integral setup. I think dA = h-y dx is correct.
 
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The point (b,h) lies on the curve. Doesn't that suggest something, like a relationship between them, which you can put in the answer?
 
Thanks for your reply, I figured it out
 
Last edited:

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