Vector field F is given byF(r) = (x, y, z + 1)and surface A is the locus of points satisfying z + x² + y² + 2√x² + y² = 8 for z > 0. (Notethat the positive square root appears in this expression.)(b) Evaluate directly (using cylindrical coordinates or otherwise) the surface integralJSIJ=where the flux is evaluated in the direction with positivez component.(c) Evaluate directly the volume-integral=F.dsJIJ (V.F) dVwhere W is the solid region lying between surface A and the (x, y)-plane.(d) Hence, without further integration, determine the value ofK==|| FBF·ds,where B is the disc of radius 2 in the (x, y)-plane, centred on the origin, with normal dS inthe positive z direction and justify your answer.

Given the vector field F(x,y,z)=(x,y,z+1).The surface A is (b)Let us evaluate the surface integral…

Answered: Vector field F is given by F(r) = (x,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

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