(c) Let M be the surface with the equation x +y° +z = 9 that is above the right triangular region with vertices (0,0), (1,0) and (1,2). (i) Write down the vector function r(r, y) and domain of the parameterization for surface M. (ii) For the vector field F =ri+yj+ (x + y) k, evaluate F. dS. M (iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral that gives the surface integral of g over M.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(c) Let M be the surface with the equation x +y° +z = 9 that is above the right triangular region with
vertices (0,0), (1,0) and (1,2).
(i) Write down the vector function r(x, y) and domain of the parameterization for surface M.
(ii) For the vector field F =ri+yj+ (x + y) k, evaluate
F. dS.
M
(iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral
that gives the surface integral of g over M.
Transcribed Image Text:(c) Let M be the surface with the equation x +y° +z = 9 that is above the right triangular region with vertices (0,0), (1,0) and (1,2). (i) Write down the vector function r(x, y) and domain of the parameterization for surface M. (ii) For the vector field F =ri+yj+ (x + y) k, evaluate F. dS. M (iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral that gives the surface integral of g over M.
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