Calculus: Moments-Are these correct ?

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SUMMARY

The discussion focuses on calculating the moments Mx and My, as well as the centroid of a lamina with a density of 15, bounded by the curves y = -x² + 1 and y = -3. The user reported their calculated values as ybar = 24 and Mx = 256, expressing uncertainty about their accuracy. The calculations involve applying specific formulas for moments and centroids in calculus, emphasizing the importance of precision in each step to avoid errors.

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  • Understanding of calculus concepts, specifically moments and centroids.
  • Familiarity with the formulas for calculating Mx and My.
  • Knowledge of how to integrate functions to find areas under curves.
  • Ability to manipulate algebraic expressions accurately.
NEXT STEPS
  • Review the formulas for calculating moments Mx and My in laminae.
  • Practice integration techniques for finding centroids of regions bounded by curves.
  • Explore examples of calculating centroids for different shapes in calculus.
  • Utilize graphing tools to visualize the bounded region and verify calculations.
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Students studying calculus, educators teaching moments and centroids, and anyone seeking to improve their integration and algebraic manipulation skills.

MitsuShai
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1. Calculate the moments Mx and My and the centroid of the lamina with density 15 that is in the shape of the region bounded by y=-x^2+1 and y=-3

I got the My and xbar. However, I keep messing up when doing the ybar and the Mx; I messed up like 5 times (no laughing). This time I got:
ybar: 24
Mx= 256

are these right?

I would show my work but that's A LOT of typing and the work on my paper is really really messing because I kept messing up. I know it's basically just plugging in numbers to the formula, but I mess up at every and any little thing.
 
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