?Consider the solid \(Q=\{(x, y, z) \mid 0 \leq x \leq 1,0 \leq y \leq 2,0 \leq z \leq

Chapter 5, Problem 338

(choose chapter or problem)

Consider the solid \(Q=\{(x, y, z) \mid 0 \leq x \leq 1,0 \leq y \leq 2,0 \leq z \leq 3\}\) with the density function ρ(x, y, z) = x + y + 1.

a. Find the mass of Q.

b. Find the moments \(M_{x y}\), \(M_{x z}\), and \(M_{y z}\) about the xy-plane, xz-plane, and yz-plane, respectively.

c. Find the center of mass of Q.

Text Transcription:

Q={(x, y, z) mid 0 leq x leq 1,0 leq y leq 2,0 leq z leq 3}

M_xy

M_xz

M_yz