5.9 Please help me answer this engineering math problem. Exercise 9Find the flux of F through Sthrough s fF.dsSF(x, y, z) = xi+yj+zk, S: z=1-x² - y², z ≥ 0.

Answered: through s ffF.ds Find the flux of F…

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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5.9 Please help me answer this engineering math problem.

Exercise 9
Find the flux of F through S
through s fF.ds
S
F(x, y, z) = xi+yj+zk, S: z=1-x² - y², z ≥ 0.

Expert Solution

Step 1: Explanation

Given that,

Assume,

$table row cell z equals h open parentheses x comma y close parentheses equals 1 minus x squared minus y squared end cell row cell Then comma end cell row cell fraction numerator partial differential z over denominator partial differential x end fraction equals g subscript x equals negative 2 x end cell row cell fraction numerator partial differential z over denominator partial differential y end fraction equals g subscript y equals negative 2 y end cell row blank row cell And comma end cell row cell nabla g equals negative fraction numerator partial differential z over denominator partial differential x end fraction i minus fraction numerator partial differential z over denominator partial differential y end fraction j plus k end cell row cell nabla g equals 2 x i plus 2 y j plus k end cell row end table$