Consider the triple integral S S SM dv where M = {(x, y, z) | x² + y² + z² ≤ 4, z ≥ 0, and x² + y² ≤ 1} Rewrite this triple integral for Cylindrical coordinate using dV coordinate using dV = p² sin(p)dpdydł (You must setup two triple integrals with the order and the coordinate systems mentioned for dV) rdzdrde and Spherical

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the triple integral
S S SM dv
where
M
{(x, y, z) | x² + y² + z² ≤ 4, z ≥ 0, and x² + y² ≤ 1}
Rewrite this triple integral for Cylindrical coordinate using dV
coordinate using dV = p² sin(p)dpdyd0
(You must setup two triple integrals with the order and the coordinate systems mentioned for dV)
=
=
rdzdrde and Spherical
Transcribed Image Text:Consider the triple integral S S SM dv where M {(x, y, z) | x² + y² + z² ≤ 4, z ≥ 0, and x² + y² ≤ 1} Rewrite this triple integral for Cylindrical coordinate using dV coordinate using dV = p² sin(p)dpdyd0 (You must setup two triple integrals with the order and the coordinate systems mentioned for dV) = = rdzdrde and Spherical
Expert Solution
Step 1

The given region is M=x,y,z| x2+y2+z24, z0, x2+y21.

To SETUP: integrals for the volume of the above region using cylindrical and spherical coordinates.

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