Set up an integral in cylindrical coordinates to evaluate xy dV where E is the region E enclosed by the cone z = 6 x² + y?, the cylinder x? + y? = 9, and the xy plane. | Choose values from the domains: r 2 0, 0 < 0< 2n, and - o < z <∞. Enter theta to denote 0 and pi to denote T. 6 - r • cos(0) sin(0) dz dr do Complete the integration to compute the volume. Enter an exact answer.

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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This is a calculus 3 (spherical and cylindrical coordinates) problem. I'm stuck in the red highlighted box. 

 

 

Set up an integral in cylindrical coordinates to evaluate
xy dV where E is the region
enclosed by the cone z =
+ y?, the cylinder x? + y? = 9, and the xy plane.
Choose values from the domains: r > 0, 0 < 0 < 2n, and – o < z < ∞. Enter theta to denote 0
and pi to denote T.
3
6 - r
cos(0) sin(0)
CoS
dz dr do
Complete the integration to compute the volume. Enter an exact answer.
Transcribed Image Text:Set up an integral in cylindrical coordinates to evaluate xy dV where E is the region enclosed by the cone z = + y?, the cylinder x? + y? = 9, and the xy plane. Choose values from the domains: r > 0, 0 < 0 < 2n, and – o < z < ∞. Enter theta to denote 0 and pi to denote T. 3 6 - r cos(0) sin(0) CoS dz dr do Complete the integration to compute the volume. Enter an exact answer.
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