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Find. a. the mass of the solid. b. the center of mass. A solid region in the first octant is bounded by the coordinate planes and the plane $x+y+z=2 .$ The density ...

Question

Find. a. the mass of the solid. b. the center of mass. A solid region in the first octant is bounded by the coordinate planes and the plane $x+y+z=2 .$ The density of the solid is $\delta(x, y, z)=2 x$.

Find. a. the mass of the solid. b. the center of mass. A solid region in the first octant is bounded by the coordinate planes and the plane $x+y+z=2 .$ The density of the solid is $\delta(x, y, z)=2 x$.



Answers

Find the mass and center of mass of the solid $ E $ with the given density function $ \rho $.

$ E $ is bounded by the parabolic cylinder $ z = 1 - y^2 $ and the planes $ x + z = 1 $, $ x = 0 $, and $ z = 0 $ ; $ \rho (x, y, z) = 4 $


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