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

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The discussion focuses on finding the exact coordinates of the centroid for a region bounded by specific curves. A user requests help in verifying their calculations, particularly for the x-coordinate, suggesting that it is better to leave it in fractional form as 1/ln(2) rather than converting it to a decimal. There is also confusion regarding the calculation of the y-coordinate, where (1/2)2 is incorrectly simplified to (1/2). Participants are encouraged to review the attached work for accuracy. The thread emphasizes the importance of precise calculations in determining centroid coordinates.
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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    new hw 8-3 prob 28.gif
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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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