1. a) Let D = {(x,y) = R : x 1, y 1}. Show...

 

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1. a) Let D = {(x,y) = R² : x ≥ 1, y ≥ 1}. Show that the improper integral 1 L6₁₂₁1 +7922 dzdy xy²) ² D is convergent and compute the value of the integral. (Ch. 14.3) (2 p) b) Let K = {−1≤ x + 2z ≤ 2, 0 ≤ −3x + y + 2z ≤ 2, 1 ≤ −x + 2y ≤ 3} and p(x,y,z) = -x + 2y be the density (mass/volume unit) of K. Find the mass of K. (Ch. 14.6, 14.7) (2p) 1. a) Let D = {(x,y) = R² : x ≥ 1, y ≥ 1}. Show that the improper integral 1 L6₁₂₁1 +7922 dzdy xy²) ² D is convergent and compute the value of the integral. (Ch. 14.3) (2 p) b) Let K = {−1≤ x + 2z ≤ 2, 0 ≤ −3x + y + 2z ≤ 2, 1 ≤ −x + 2y ≤ 3} and p(x,y,z) = -x + 2y be the density (mass/volume unit) of K. Find the mass of K. (Ch. 14.6, 14.7) (2p)

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Part A Part B Solution x y ER x1 921 let D The improper integra... View the full answer