Verify the formula /F-n ds = div F dV in the Divergence Theorem by evaluating the surface integral and the triple integral. F(r, y, z) = 2ri – yzj + z°k where o is the paraboloid z = x² + y? capped by the disk x? + y < 4 in the plane z = 4.

Verify the formula /F-n ds = div F dV in the Divergence Theorem by evaluating the surface integral and the triple integral. F(r, y, z) = 2ri – yzj + z°k where o is the paraboloid z = x² + y? capped by the disk x? + y < 4 in the plane z = 4.

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

Verify the formula
F.n dS =
div F dV
in the Divergence Theorem by evaluating the surface integral and the
triple integral.
F(r, y, z) = 2ri – yzj + z°k
where o is the paraboloid z = x² + y capped by the disk x? + y <4
in the plane z =
4.
F.n dS =
%3D
div F dV

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