Vector field F is given by F(r) = (x+2, 0, z+2) and surface A is the locus of points satisfying z + x² + y² = 3 + 2√x² + y² for z > 0. (Note that the positive square root appears in this expression.) (a) Sketch by hand (not assisted by any software) surface A. (b) Evaluate directly (using cylindrical coordinates or otherwise) the surface integral I = SS A F.ds where the flux is evaluated in the direction with positive z component. (c) Evaluate directly the volume-integral J = SSS W (☑ F) dV where W is the solid region lying between surface A and the (x, y)-plane. (d) Hence, without further integration, determine the value of K = SS B F.dS, where B is the disc of radius 3 in the (x, y)-plane, centred on the origin, with normal ds in the positive z direction and justify your answer.

Vector field F is given by F(r) = (x+2, 0, z+2) and surface A is the locus of points satisfying z + x² + y² = 3 + 2√x² + y² for z > 0. (Note that the positive square root appears in this expression.) (a) Sketch by hand (not assisted by any software) surface A. (b) Evaluate directly (using cylindrical coordinates or otherwise) the surface integral I = SS A F.ds where the flux is evaluated in the direction with positive z component. (c) Evaluate directly the volume-integral J = SSS W (☑ F) dV where W is the solid region lying between surface A and the (x, y)-plane. (d) Hence, without further integration, determine the value of K = SS B F.dS, where B is the disc of radius 3 in the (x, y)-plane, centred on the origin, with normal ds in the positive z direction and justify your answer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 20RE

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