66-69. Mass and center of mass Let S be a surface that represents a thin shell with density p. The moments about the coordinate planes (see Section 16.6) are My, = ls xp(x, y. z) dS, M = lsyp(x, y, z) dS, and My = Sls zp(x, y, z) dS. The coordinates of the center of mass of %3D and z = m M, , where m is the mass of the shell are i = ỹ = m m the shell. Find the mass and center of mass of the following shells. Use symmetry whenever possible. The cylinder x? + y² = a², 0 s z s 2, with density p(х, у, г) — 1 + г

Question
66-69. Mass and center of mass Let S be a surface that represents a
thin shell with density p. The moments about the coordinate planes (see
Section 16.6) are My, = ls xp(x, y. z) dS, M = lsyp(x, y, z) dS,
and My = Sls zp(x, y, z) dS. The coordinates of the center of mass of
%3D
and z =
m
M,
, where m is the mass of
the shell are i =
ỹ =
m
m
the shell. Find the mass and center of mass of the following shells. Use
symmetry whenever possible.
The cylinder x? + y² = a², 0 s z s 2, with density
p(х, у, г) — 1 + г
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Applications of Integration

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66-69. Mass and center of mass Let S be a surface that represents a thin shell with density p. The moments about the coordinate planes (see Section 16.6) are My, = ls xp(x, y. z) dS, M = lsyp(x, y, z) dS, and My = Sls zp(x, y, z) dS. The coordinates of the center of mass of %3D and z = m M, , where m is the mass of the shell are i = ỹ = m m the shell. Find the mass and center of mass of the following shells. Use symmetry whenever possible. The cylinder x? + y² = a², 0 s z s 2, with density p(х, у, г) — 1 + г