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[ 13/12/ 2 -2. 2 -2./y2. √2 LV₂ g(x, y, z) dz dx dy + y2⁹(x, y, z) g(x, y, z) dy dz dx √z j√z- g(x, y, z) dx dz dy -√z-x² |√Z | √z-y² g(x, y, z) dy dx dz (Y,Z) alx x 7) dx dy dz

[ 13/12/ 2 -2. 2 -2./y2. √2 LV₂ g(x, y, z) dz dx dy + y2⁹(x, y, z) g(x, y, z) dy dz dx √z j√z- g(x, y, z) dx dz dy -√z-x² |√Z | √z-y² g(x, y, z) dy dx dz (Y,Z) alx x 7) dx dy dz

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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Question
Rewrite the following iterated integral using five different orders of integration. 121 4 13626 4 2 √4x² 4 L 4 12. + 1292 + y g(x, y, z) dz dy dx g(x, y, z) dz dx dy Vz g(x, y, z) dy dz dx g(x, y, z) dx dz dy g(x, y, z) dy dx dz g(x, y, z) dx dy dz
Transcribed Image Text:Rewrite the following iterated integral using five different orders of integration. 121 4 13626 4 2 √4x² 4 L 4 12. + 1292 + y g(x, y, z) dz dy dx g(x, y, z) dz dx dy Vz g(x, y, z) dy dz dx g(x, y, z) dx dz dy g(x, y, z) dy dx dz g(x, y, z) dx dy dz
Expert Solution
Step 1

Rewrite the integral ∫-22∫-4-x24-x2∫x2+y24 gx,y,z dz dy dx

1) Here y=-4-x2 , y=4-x2 and x=-2 , x=2

Implies, 

y2=4-x2⇒x2=4-y2⇒x=±4-y2

∫-22∫-4-y24-y2∫x2+y24 gx,y,z dz dx dy

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