a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF.ds where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2.
a) Suppose that F(x, y, z) = (x² + y)i + z²j+(e* -z)k i) Find the divergence of F(x, y, z). Hence, by using the Divergence Theorem, evaluate fF.ds where is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3, y = 1 and z = 2.
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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Please solve all the question.
Transcribed Image Text:a) Suppose that
F(x, y, z) = (x² + y)i + z²j+(e* -z)k
i) Find the divergence of F(x, y, z).
Hence, by using the Divergence Theorem, evaluate fF-fids where is the
surface of the rectangular solid bounded by the coordinate planes and the planes x
= 3, y = 1 and z = 2.
b) Let R be the region between circles x² + y² = 36 and x² + y² =1. Sketch the region
and evaluate the line integral [2xydy + (x²+2x)dy using the Green's Theorem
c) Use the Stoke's Theorem to evaluate [F. dr where F(x, y, z) = -y² + zj+ xk and C
be the positive oriented triangle lying on the plane 2x +2y+z= 6 bounded by the
coordinate planes.
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Solve b) and c)
Transcribed Image Text:a) Suppose that
F(x, y, z) = (x² + y)i + z²j+(e* -z)k
i) Find the divergence of F(x, y, z).
Hence, by using the Divergence Theorem, evaluate fF-fids where is the
surface of the rectangular solid bounded by the coordinate planes and the planes x
= 3, y = 1 and z = 2.
b) Let R be the region between circles x² + y² = 36 and x² + y² =1. Sketch the region
and evaluate the line integral [2xydy + (x²+2x)dy using the Green's Theorem
c) Use the Stoke's Theorem to evaluate [F. dr where F(x, y, z) = -y² + zj+ xk and C
be the positive oriented triangle lying on the plane 2x +2y+z= 6 bounded by the
coordinate planes.
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