1.4. Let U be an open set in R³, and let S be a smooth oriented surface in U with orienting normal vector field n. Let F be a continuous vector field on U. If F(x) = n(x) for all x in S, prove that ff FdS Area (S). =
1.4. Let U be an open set in R³, and let S be a smooth oriented surface in U with orienting normal vector field n. Let F be a continuous vector field on U. If F(x) = n(x) for all x in S, prove that ff FdS Area (S). =
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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Transcribed Image Text:1.4. Let U be an open set in R³, and let S be a smooth oriented surface in U with orienting normal
vector field n. Let F be a continuous vector field on U. If F(x) = n(x) for all x in S, prove
that ffs F. ds = Area (S).
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