7. So is the part of the paraboloid z = 1 − x² - y² that lies above the xy-plane. (a) Find the area of So; (b) Assuming that So has upward orientation, evaluate the surface integral so F. n dS for F(x, y, z) = (y, x, z). 8. Let n be the outward unit normal (normal away from the origin) of the hemisphere So : x² + y² + x² = 16, y ≥ 0, and let F(x, y, z) zei + x cos yj + xz sin yk. Use Stokes' Theorem to find the value of ffs (V× F). n dS.
7. So is the part of the paraboloid z = 1 − x² - y² that lies above the xy-plane. (a) Find the area of So; (b) Assuming that So has upward orientation, evaluate the surface integral so F. n dS for F(x, y, z) = (y, x, z). 8. Let n be the outward unit normal (normal away from the origin) of the hemisphere So : x² + y² + x² = 16, y ≥ 0, and let F(x, y, z) zei + x cos yj + xz sin yk. Use Stokes' Theorem to find the value of ffs (V× F). n dS.
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:7. So is the part of the paraboloid z = 1- x² - y² that lies above the xy-plane.
(a) Find the area of So;
(b) Assuming that So has upward orientation, evaluate the surface integral JS, F.
n dS for F(x, y, z) = (y, x, z).
8. Let n be the outward unit normal (normal away from the origin) of the hemisphere
So : x² + y² + z² = 16, y ≥ 0, and let F(x, y, z) = ze³i+ x cos yj + xz sin yk. Use
Stokes' Theorem to find the value of ffs (V x F). n ds.
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