Center of Mass for a Planar Region in Cartesian Coordinates
Description
Determine x&conjugate0; and y&conjugate0;, the center of mass coordinates for a planar region in Cartesian Coordinates.
Center of Mass for Planar Region in Cartesian Coordinates
Density:
1
Region: ux≤y≤vx,a≤x≤b
ux
x2
vx
x
a
0
b
Moments÷Mass:
Inert Integral - dy dx
StudentMultivariateCalculusCenterOfMass, x=..,y=..,output=integral
∫01∫x2xxⅆyⅆx∫01∫x2x1ⅆyⅆx,∫01∫x2xyⅆyⅆx∫01∫x2x1ⅆyⅆx
Explicit values for x&conjugate0; and y&conjugate0;
StudentMultivariateCalculusCenterOfMass,x=..,y=..
12,25
Plot:
StudentMultivariateCalculusCenterOfMass,x=..,y=..,output=plot,caption=
Commands Used
Student[MultivariateCalculus][CenterOfMass]
Related Task Templates
Multivariate Calculus > Multiple Integration > Cartesian 2-D
See Also
Student[MultivariateCalculus], Student[MultivariateCalculus][MultiInt]
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