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 isthe 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 pointinginwards 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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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 = 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).