Consider I=E∫x3dx1dx2dx3, where E: x12 + x22 ≤ x23, 0 ≤ x3 ≤ 1,that is, E is the solid bounded by the cone x12 + x22 = x23, the plane x3 = 0, and the plane x3=1. a) Use cylindrical coordinates to calculate I. b) Calculate I without using cylindrical coordinates.
Consider I=E∫x3dx1dx2dx3, where E: x12 + x22 ≤ x23, 0 ≤ x3 ≤ 1,that is, E is the solid bounded by the cone x12 + x22 = x23, the plane x3 = 0, and the plane x3=1. a) Use cylindrical coordinates to calculate I. b) Calculate I without using cylindrical coordinates.
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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Consider I=E∫x3dx1dx2dx3, where E: x12 + x22 ≤ x23, 0 ≤ x3 ≤ 1,that is, E is the solid bounded by the cone x12 + x22 = x23, the plane x3 = 0, and the plane x3=1.
a) Use cylindrical coordinates to calculate I.
b) Calculate I without using cylindrical coordinates.
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