Let J = √x² + y2 + z² dV, Where E is the region given by : E x² + y² + z² ≤2 Expressed in Spherical Coordinates (p, , 0), the integral J is equivalent to : 2π -π/2 1²² 1/² 1/2 p²sin(p) dp do de 0 0 -2 2 p²cos(p) dp do de π 0 2π π/2 √2 p*cos(p) dp do de √₂ p³cos(p) dp do de 0 0 -√2 2π √2 offr Sp³sin(c) dp do de 0 0 0 T 0 0 0 0 T S™

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let J= √√x² + y2 + z² dV, Where E is the region given by :
E
x² + y² + z² ≤ 2
Expressed in Spherical Coordinates (p, , 0), the integral J is equivalent to :
2π π/2 2
(0²1² p²sin(9) dp do de
-2
TC
2
ST
p²cos(p) dp do de
0
0 0
2π .π/2 √√₂
p³cos(p) dp do de
0
0
0
√₂
Sp³cos(p) dp do de
0 -√2
√₂
p³sin(q) dp do de
2π
0
2π TC
0
00
Transcribed Image Text:Let J= √√x² + y2 + z² dV, Where E is the region given by : E x² + y² + z² ≤ 2 Expressed in Spherical Coordinates (p, , 0), the integral J is equivalent to : 2π π/2 2 (0²1² p²sin(9) dp do de -2 TC 2 ST p²cos(p) dp do de 0 0 0 2π .π/2 √√₂ p³cos(p) dp do de 0 0 0 √₂ Sp³cos(p) dp do de 0 -√2 √₂ p³sin(q) dp do de 2π 0 2π TC 0 00
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