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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F306db17a-c2a3-4020-aada-7a92dff91485%2F457105dc-db14-460a-9d90-2d0d16ab7b0b%2Fuy8tsv4_processed.png&w=3840&q=75)
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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