9. Let G CR be a solid and let o = ƏG be the boundary surface of G, oriented by the outward normal n. Let f : G → R be a differentiable function with continuous partial derivatives. Prove: fn dS Note that the surface and triple integrals of vector functions are defined by integrating the scalar function in each component. [Hint: One way to approach this problem is to dot both sides with an arbitrary constant vector à E R³. You also need to use a famous theorem from the class.]
9. Let G CR be a solid and let o = ƏG be the boundary surface of G, oriented by the outward normal n. Let f : G → R be a differentiable function with continuous partial derivatives. Prove: fn dS Note that the surface and triple integrals of vector functions are defined by integrating the scalar function in each component. [Hint: One way to approach this problem is to dot both sides with an arbitrary constant vector à E R³. You also need to use a famous theorem from the class.]
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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![9. Let G CR be a solid and let o = ƏG be the boundary surface of G,
oriented by the outward normal n. Let f : G → R be a differentiable
function with continuous partial derivatives. Prove:
fn dS
Note that the surface and triple integrals of vector functions are defined
by integrating the scalar function in each component. [Hint: One way
to approach this problem is to dot both sides with an arbitrary constant
vector à E R³. You also need to use a famous theorem from the class.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9107650-c916-4694-865d-5231de163068%2F107bcdd9-b8df-4974-95d0-71bd356395e9%2Fulai0ps.png&w=3840&q=75)
Transcribed Image Text:9. Let G CR be a solid and let o = ƏG be the boundary surface of G,
oriented by the outward normal n. Let f : G → R be a differentiable
function with continuous partial derivatives. Prove:
fn dS
Note that the surface and triple integrals of vector functions are defined
by integrating the scalar function in each component. [Hint: One way
to approach this problem is to dot both sides with an arbitrary constant
vector à E R³. You also need to use a famous theorem from the class.]
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