Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axi...

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Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axi...

Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis.

(a) Find an expression for the mass of E as a triple integral. Then briefly explain why this integral is difficult to compute.

(b) (8 points) Describe the solid E using cylindrical coordinates.Then express the mass of E as a triple integral in cylindrical coordinates and evaluate this integral.

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Answer 1

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Mass- densityXvolume density-pox distance from z axis let the coordinates of point be (x,y,z) and (0,0,2) be any point in the M- 1-y 8k Iny dy 0 Difficult to integrate however using cylindrical coordinates mass M-I//ρdxdydz kr (rdrdoda) 2drdodz

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Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axi...

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Add Answer to: Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axi...

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Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axi...