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Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the cylinder x2 + y2 = 4 and above the xy-plane

Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the cylinder x2 + y2 = 4 and above the xy-plane

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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### Evaluate the Surface Integral Evaluate the surface integral: \[ \iint_{S} y^2 \, dS \] where \( S \) is the part of the sphere defined by the equation \( x^2 + y^2 + z^2 = 16 \). This region lies inside the cylinder given by \( x^2 + y^2 = 4 \) and is positioned above the \( xy \)-plane.
Transcribed Image Text:### Evaluate the Surface Integral Evaluate the surface integral: \[ \iint_{S} y^2 \, dS \] where \( S \) is the part of the sphere defined by the equation \( x^2 + y^2 + z^2 = 16 \). This region lies inside the cylinder given by \( x^2 + y^2 = 4 \) and is positioned above the \( xy \)-plane.
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