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The region D3 bounded by the cone z² = x² + y² and the parabola z = 2-x² - y² The region D4 in the first octant bounded by the cylinder x² + y² = 4, the paraboloid z = 8 - x² - y² and the planes x = y, z = 0, and x -

The region D3 bounded by the cone z² = x² + y² and the parabola z = 2-x² - y² The region D4 in the first octant bounded by the cylinder x² + y² = 4, the paraboloid z = 8 - x² - y² and the planes x = y, z = 0, and x -

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do part 3 & 4
A)Determine the boundary limits of the following regions in spaces. The region D₁ bounded by the planes x + 2y + 3z = 6 and the coordinate planes. - ✪ The region D₂ bounded by the cylinders y = x² and y = 4 — x², and the planes x +2y + z = 1 and x+y+z= 1. ✪ The region D3 bounded by the cone z² = x² + y² and the parabola z = 2-x² - y² The region D4 in the first octant bounded by the cylinder - x² + y² = 4, the paraboloid z = 8 – x² - y² and the planes x = y, z = 0, and x = 0. B) Calculate the following integrals JJJ dV, III yov III xy D3 xy dV, 11/₂" JJJ. dV,
Transcribed Image Text:A)Determine the boundary limits of the following regions in spaces. The region D₁ bounded by the planes x + 2y + 3z = 6 and the coordinate planes. - ✪ The region D₂ bounded by the cylinders y = x² and y = 4 — x², and the planes x +2y + z = 1 and x+y+z= 1. ✪ The region D3 bounded by the cone z² = x² + y² and the parabola z = 2-x² - y² The region D4 in the first octant bounded by the cylinder - x² + y² = 4, the paraboloid z = 8 – x² - y² and the planes x = y, z = 0, and x = 0. B) Calculate the following integrals JJJ dV, III yov III xy D3 xy dV, 11/₂" JJJ. dV,
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