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4. Evaluate the surface integral f dS where, Σ (a) f(x, y, z) = xz and E is the boundary of the region D in R³ inside the cylinder x2 + y² planes z = 0 and z = x+2. 1 between the = x2 and E is the boundary of the region D in R³ inside the cone z? = x² + y? and between the (b) f(x,y, z) planes z = 1 and z = 2.

4. Evaluate the surface integral f dS where, Σ (a) f(x, y, z) = xz and E is the boundary of the region D in R³ inside the cylinder x2 + y² planes z = 0 and z = x+2. 1 between the = x2 and E is the boundary of the region D in R³ inside the cone z? = x² + y? and between the (b) f(x,y, z) planes z = 1 and z = 2.

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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4. Evaluate the surface integral [S f dS where, Σ (a) f(x, y, z) = xz and E is the boundary of the region D in R³ inside the cylinder x2 + y? planes z = 0 and z = x + 2. = 1 between the (b) f(x, y, z) = x² and E is the boundary of the region D in R³ inside the cone z? planes x² + y? and between the z = 1 and z = 2.
Transcribed Image Text:4. Evaluate the surface integral [S f dS where, Σ (a) f(x, y, z) = xz and E is the boundary of the region D in R³ inside the cylinder x2 + y? planes z = 0 and z = x + 2. = 1 between the (b) f(x, y, z) = x² and E is the boundary of the region D in R³ inside the cone z? planes x² + y? and between the z = 1 and z = 2.
Definition: Consider an oriented surface E given by x = g(u, v), (u, v) E Duv, with g of class C, and a vector field F continuous on E. The surface integral of F over E is defined by || F(g(u, v)) · (u dudv. dv (3.23) F. ndS Σ Duv
Transcribed Image Text:Definition: Consider an oriented surface E given by x = g(u, v), (u, v) E Duv, with g of class C, and a vector field F continuous on E. The surface integral of F over E is defined by || F(g(u, v)) · (u dudv. dv (3.23) F. ndS Σ Duv
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