Need someone to check my work: Finding the exact coordinates of the centroid

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SUMMARY

The discussion focuses on calculating the exact coordinates of the centroid for a region bounded by specific curves. The user suggests that the x-coordinate, \overline{x}, should be expressed as 1/ln(2) instead of the decimal approximation of 1.44. For the y-coordinate, \overline{y}, there is confusion regarding the simplification of (1/2)2 to (1/2). The conversation highlights the importance of precise mathematical expressions in centroid calculations.

PREREQUISITES
  • Understanding of centroid calculations in calculus
  • Familiarity with integration techniques for area under curves
  • Knowledge of logarithmic functions and their properties
  • Ability to interpret and sketch bounded regions in the Cartesian plane
NEXT STEPS
  • Review the process of finding centroids using integration techniques
  • Study the properties of logarithmic functions, specifically ln(x)
  • Practice sketching regions defined by curves to visually estimate centroids
  • Explore common pitfalls in simplifying expressions in calculus
USEFUL FOR

Students in calculus courses, educators teaching geometry and calculus, and anyone involved in mathematical problem-solving related to centroids and area calculations.

jimen113
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1. Homework Statement [/b]
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid:


Homework Equations


I don't have the answer for this problem to check my work.


The Attempt at a Solution


see attachment
 

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For \overline{x}, I would suggest that leaving the answer as 1/ln(2) would be preferable to "1.44".

For \overline{y}, (1/2)2 seems to mysteriously become (1/2).
 

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