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
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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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.
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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