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i) Evaluate the surface integral where F = (x,y,zx) and S has upward orientation. S is the part of the paraboloid Z= 2-- above the square 0

i) Evaluate the surface integral where F = (x,y,zx) and S has upward orientation. S is the part of the paraboloid Z= 2-- above the square 0

Advanced Engineering Mathematics
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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2. i) Evaluate the surface integral F - aš where F = (x, y, zx) and S has upward orientation. S is the part of the paraboloid Z = 2-x? -y° above the square 0<x<1,0<y<1. (ii) Find the flux of the vector field F = (z, zy, x) across of the upper hemisphere (with upward orientation) x² +y? +z? = 4 with z 20. (Hint: parametrize the surface).
Transcribed Image Text:2. i) Evaluate the surface integral F - aš where F = (x, y, zx) and S has upward orientation. S is the part of the paraboloid Z = 2-x? -y° above the square 0<x<1,0<y<1. (ii) Find the flux of the vector field F = (z, zy, x) across of the upper hemisphere (with upward orientation) x² +y? +z? = 4 with z 20. (Hint: parametrize the surface).
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