a) Evaluate [-ri-yj+2: k) - n ds, (-a i- where a is the portion of the paraboloid z = 3r + 3y between the planes z = 0 and z = 6 with n, the unit normal pointed in the positive z-axis direction.
a) Evaluate [-ri-yj+2: k) - n ds, (-a i- where a is the portion of the paraboloid z = 3r + 3y between the planes z = 0 and z = 6 with n, the unit normal pointed in the positive z-axis direction.
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:a) Evaluate
/|(-ri-
i-yj+2: k) · n dS,
where o is the portion of the paraboloid z = 3r + 3y? between the
planes z = 0 and z = 6 with n, the unit normal pointed in the positive
z-axis direction.
b) Given F(x, y, z) = ( + cosh z) i+ (2y3 – 3r*y)j – (2 + 4y°z) k. Use
Gauss's theorem to calculate /F
.n dS where n is the outward
unit normal of a, the surface bounded by the planes, r = 0, z = 0 and
I+: = 6, and the parabolic cylinder r = 4 - y.
c) Use Stokes' theorem to evaluate
(ry – y) i – In zj+ (r+a) k) dr,
where C is the intersection between the plane z = 3 and the cylinder
+ (y– 1) = 1 with the anticlockwise orientation viewed from above.
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