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1. (i) Sketch by hand (not by computer) the surface A given by x² + y² − log(e¹ —– z) = = 0 for z> 0 where, as usual, log represents the natural logarithm. Then calculate directly (using cylindrical coordinates and integrating with respect to z first, or otherwise) the surface integral where I = P VETE"). F 2 x² + y² (ii) Consider the disc in the (x, y)-plane, centred on the origin, with radius 2 and denote this B. Evaluate [[₁ B SS F.ds, A x² + y² Io = F.ds, for the field defined in part (i). (iii) Hence, without further integration, determine the value of

1. (i) Sketch by hand (not by computer) the surface A given by x² + y² − log(e¹ —– z) = = 0 for z> 0 where, as usual, log represents the natural logarithm. Then calculate directly (using cylindrical coordinates and integrating with respect to z first, or otherwise) the surface integral where I = P VETE"). F 2 x² + y² (ii) Consider the disc in the (x, y)-plane, centred on the origin, with radius 2 and denote this B. Evaluate [[₁ B SS F.ds, A x² + y² Io = F.ds, for the field defined in part (i). (iii) Hence, without further integration, determine the value of

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 43E
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(iii) Hence, without further integration, determine the value of J SIS (V.F) dV, W where W is the solid region lying between the surface A of part (i) and the (x, y)-plane and justify your answer. Then confirm this through direct calculation of the integral.
Transcribed Image Text:(iii) Hence, without further integration, determine the value of J SIS (V.F) dV, W where W is the solid region lying between the surface A of part (i) and the (x, y)-plane and justify your answer. Then confirm this through direct calculation of the integral.
1. (i) Sketch by hand (not by computer) the surface A given by x² + y² − log(e² − z) = 0 for z > 0 where, as usual, log represents the natural logarithm. Then calculate directly (using cylindrical coordinates and integrating with respect to z first, or otherwise) the surface integral where 1 I F = [[ ₁ A Y "=(√₁²TE² VETE"²) + + Io = F.dS, (ii) Consider the disc in the (x, y)-plane, centred on the origin, with radius 2 and denote this B. Evaluate JS B = F.dS, for the field defined in part (i). (iii) Hence, without further integration, determine the value of
Transcribed Image Text:1. (i) Sketch by hand (not by computer) the surface A given by x² + y² − log(e² − z) = 0 for z > 0 where, as usual, log represents the natural logarithm. Then calculate directly (using cylindrical coordinates and integrating with respect to z first, or otherwise) the surface integral where 1 I F = [[ ₁ A Y "=(√₁²TE² VETE"²) + + Io = F.dS, (ii) Consider the disc in the (x, y)-plane, centred on the origin, with radius 2 and denote this B. Evaluate JS B = F.dS, for the field defined in part (i). (iii) Hence, without further integration, determine the value of
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