Let the surface Σ be the solid bounded by the paraboloid z “ 1 ´ x2 ´ y2 and the xy´plane. Computethe outward flux of F~ “ x2x3 ` y3, y3 ` z3, 3y2zy across Σ. 3. Let the surface E be the solid bounded by the paraboloid z = 1 – 22 – y² and the ry-plane. Computethe outward flux of F = (2x³ + y³, y³ + 2³, 3y²z) across E.

Use Gauss divergence theorem to compute the outward flux.

Answered: 3. Let the surface E be the solid…

3. Let the surface E be the solid bounded by the paraboloid z = 1 – 22 – y² and the ry-plane. Compute the outward flux of F = (2x³ + y³, y³ + 2³, 3y²z) across E.

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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Question

Let the surface Σ be the solid bounded by the paraboloid z “ 1 ´ x
2 ´ y
2 and the xy´plane. Compute
the outward flux of F~ “ x2x
3 ` y
3
, y3 ` z
3
, 3y
2
zy across Σ.

3. Let the surface E be the solid bounded by the paraboloid z = 1 – 22 – y² and the ry-plane. Compute
the outward flux of F = (2x³ + y³, y³ + 2³, 3y²z) across E.

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