Question

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 .

Answer #1

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 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.
D is the triangular region with vertices (0, 0), (2, 1), (0, 3);
ρ(x, y) = 8(x + y)
M =
(X,Y)=

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, 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

A lamina with constant density ρ(x,
y) = ρ occupies the given region. Find the
moments of inertia Ix and
Iy and the radii of gyration x and
y.
The region under the curve y = 4 sin(x) from
x = 0 to x = π.

A lamina with constant density ρ(x, y) = ρ occupies the given
region. Find the moments of inertia Ix and Iy and the radii of
gyration x double bar and y double bar. The rectangle 0 ≤ x ≤ 2b, 0
≤ y ≤ 5h.
Ix
=
Iy
=
=
=

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

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.

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