Question

3. Use double integrals to find the center of mass, (xcm, ycm), of a lamina with density function ρ = x bounded by y = x^2 , x = 0 and y = 1.

Answer #1

Find the mass and center of mass of the lamina bounded by the
graphs of the equations for the given density.
y = 7x, y = 7x3, x ≥
0, y ≥ 0, ρ = kxy

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function ρ.
D is bounded by the parabolas y = x2 and x =
y2; ρ(x, y) = 19 sqt(x)

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function ρ.
D is the triangular region with vertices (0, 0), (2, 1), (0, 3);
ρ(x, y) = 8(x + y)
M =
(X,Y)=

Find the center mass of the solid bounded by planes x+y+z=1, x=0
y=0, and z=0, assuming a mass density of ρ(x,y,z)=7sqrt(z)
Xcm
Ycm
Z cm

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function ρ.
D is the triangular region enclosed by the
lines y = 0, y =
4x, and, x +
4y = 1; ρ(x,
y) = x

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function ρ. where D is the
triangular region enclosed by the lines x = 0, y = x, and 2x + y =
6 and ρ(x, y) = 6x 2 .

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function
ρ.
D is the triangular region enclosed by the
lines x = 0, y =
x, and 2x
+ y =
6; ρ(x, y)
= 6x2

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function, if D is bounded by the
parabola y=4-x^2 and the x-axis. p(x,y)=y

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function, if D is bounded by the
parabola y=4-x^2 and the y-axis. p(x,y)=y

5. Find the mass of the lamina which is bounded by y = 9 − x^2
and x-axis if ρ(x, y) = y.
6. Find the center of mass for the lamina in question 5.

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