A) Determine the boundary limits of the following regions in spaces. = 6 and the The region D₁ bounded by the planes x + 2y + 3z: 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.
A) Determine the boundary limits of the following regions in spaces. = 6 and the The region D₁ bounded by the planes x + 2y + 3z: 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.
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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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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