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Let C be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If h has continuous partial derivatives on R, and F(x, y, z) is continuous on C , then ſf F(x, y, z)dS = ſf F(h(y, z), y, с R where dA = dxdz or dA 9 = dzdx

Let C be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If h has continuous partial derivatives on R, and F(x, y, z) is continuous on C , then ſf F(x, y, z)dS = ſf F(h(y, z), y, с R where dA = dxdz or dA 9 = dzdx

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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Let C be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If ʼn has continuous partial derivatives on R, and F (x, y, z) is continuous on C then 9 SS ff F(x, y, z)dS = ff F(h(y, z), y, с R where dA = dxdz or dA = dzdx 9
Transcribed Image Text:Let C be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If ʼn has continuous partial derivatives on R, and F (x, y, z) is continuous on C then 9 SS ff F(x, y, z)dS = ff F(h(y, z), y, с R where dA = dxdz or dA = dzdx 9
The volume of the space region D is the triple integral over D of the constant valued function f(x, y, z) = 1.
Transcribed Image Text:The volume of the space region D is the triple integral over D of the constant valued function f(x, y, z) = 1.
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