Centroid Position of a Lamina Bounded by a Curve

  • #1
Alex_Neof
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2

Homework Statement



A lamina is bounded by the x-axis, the y-axis, and the curve ##y = 4 -x^2.## Determine the centroid position ##(\bar{x},\bar{y})## of the lamina.

Homework Equations



## A = \int_a^b (f(x) - g(x)) dx ## (Area)

##\bar{x} = \frac{1}{A}\int_a^b x(f(x) - g(x)) dx ##

##\bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}(f(x)^2 - g(x)^2) dx ##

The Attempt at a Solution



I made a sketch and determined ## a = 0## and ##b = 2 ## for the limits.

Then just plugged into the above equations.

With this I determined the area to be ##A=16/3##

##\bar{x} = \frac{3}{4} ##

##\bar{y} = \frac{8}{5}##

Therefore centroid position is ##(\frac{3}{4},\frac{8}{5})##

Could someone kindly verify this?
 
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  • #2
Everything looks good at a glance.
 
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  • #3
It is correct, thank you :smile:. I used an online calculator to verify it. I'll write out a solution for any future viewers.
 
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