Consider the solid G2 enclosed by the xy-plane and the paraboloid z = 6y - x² - y² whose density any point (x, y, z) is 8(x, y, z) = yz². Set up an iterated triple integral in cylindrical coordinates that gives the moment of mass of G₂ about the yz-plane. Evaluate the following iterated triple integrals using spherical coordinates. 12-r ****** *** -2√3 Jo 16-2²-y² 1 - dz dy dx

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the solid G₂ enclosed by the xy-plane and the paraboloid z = 6y - x² - y² whose
density any point (x, y, z) is 8(x, y, z) = yz². Set up an iterated triple integral in cylindrical
coordinates that gives the moment of mass of G₂ about the yz-plane.
Evaluate the following iterated triple integrals using spherical coordinates.
4+√/16-a²-y²
-2√3.
12-
6
1
-
2
dz dy dx
Transcribed Image Text:Consider the solid G₂ enclosed by the xy-plane and the paraboloid z = 6y - x² - y² whose density any point (x, y, z) is 8(x, y, z) = yz². Set up an iterated triple integral in cylindrical coordinates that gives the moment of mass of G₂ about the yz-plane. Evaluate the following iterated triple integrals using spherical coordinates. 4+√/16-a²-y² -2√3. 12- 6 1 - 2 dz dy dx
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