Evaluate the following surface integrals: || F. dS. (a) F = ri + yj + zk and S is the part of the paraboloid z = 4 – a² – y? with (x, y) € [0, 1]² and n is the unit normal pointing upwards. For example, n(0,0, 1) = (0, 0, 1).
Evaluate the following surface integrals: || F. dS. (a) F = ri + yj + zk and S is the part of the paraboloid z = 4 – a² – y? with (x, y) € [0, 1]² and n is the unit normal pointing upwards. For example, n(0,0, 1) = (0, 0, 1).
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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![Evaluate the following surface integrals: ||
F. dS.
(a) F = xi + yj + zk and S is the part of the paraboloid z = 4 – x2 – y² with (x, y) E [0, 1]² and n is
the unit normal pointing upwards. For example, n(0,0, 1) = (0,0, 1).
(b) F = x²i+y*j+z²k and S is the portion of the cone z2 = x? + y? where 1< z < 4 andn is pointing
inwards to the cone. For example, n(1,0, 1) = (-,0, ).
(c) F = 3ry²i + 3x²yj+ z*k and S is the unit sphere with the outward pointing normal n(x, y, z) =
(x, y, z).
'(주'0우-) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12f51b64-c3b4-40b6-b565-16b387e10bf1%2F50075d60-2b0e-4e96-b524-0c2ebe665b5b%2Fnqkjop6_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluate the following surface integrals: ||
F. dS.
(a) F = xi + yj + zk and S is the part of the paraboloid z = 4 – x2 – y² with (x, y) E [0, 1]² and n is
the unit normal pointing upwards. For example, n(0,0, 1) = (0,0, 1).
(b) F = x²i+y*j+z²k and S is the portion of the cone z2 = x? + y? where 1< z < 4 andn is pointing
inwards to the cone. For example, n(1,0, 1) = (-,0, ).
(c) F = 3ry²i + 3x²yj+ z*k and S is the unit sphere with the outward pointing normal n(x, y, z) =
(x, y, z).
'(주'0우-) =
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