Let Σ be part of the paraboloid z = 3 - x² – y² that lies above the xy-plane, oriented downward, along with the disk x² + y² ≤ 3 on the xy-plane, oriented upward. Using an appropriate theorem, turn the surface integral [[(xi + (y+z)j — z²k) · ndS - into a triple integral in cylindrical coordinates. Name the theorem you are using, and as usual, include all relevant diagrams. Do not evaluate the integral!

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let be part of the paraboloid z =
3 - x² - y²
that lies above the xy-plane, oriented downward,
along with the disk x² + y² ≤ 3 on the xy-plane,
2
oriented upward. Using an appropriate theorem, turn
the surface integral
[[ (xi + (y + z)j – z²k) • n dS
into a triple integral in cylindrical coordinates. Name
the theorem you are using, and as usual, include all
relevant diagrams. Do not evaluate the integral!
Transcribed Image Text:Let be part of the paraboloid z = 3 - x² - y² that lies above the xy-plane, oriented downward, along with the disk x² + y² ≤ 3 on the xy-plane, 2 oriented upward. Using an appropriate theorem, turn the surface integral [[ (xi + (y + z)j – z²k) • n dS into a triple integral in cylindrical coordinates. Name the theorem you are using, and as usual, include all relevant diagrams. Do not evaluate the integral!
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