QUESTION B-#r.F-n da of the field F-(x-3xy) + (y-ay²2) + (xyz²+2xz) & outwards through the surface of the sold bounded by theplanes y + z 2 x 2 and 2-1 and the coordinate planes as an single iterated integral. Do not evaluate the aerated integral. See picture as an aldez = 1Express the fluxy+z= 2Wx = 2True/False - You will submit your answer and sufficient work to fully support your answer while using correct notation.True

Answered: Image /qna-images/answer/b4c557bd-11fc-4cda-bccd-7c8cd97ef0d4.jpg

Answered: #r.. F-n do of the field F-(x-3xy³) +…

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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Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 3yi + (5 - 5x)j + (z² − 2)k S: r(0,0) = (√5 sin & cos 0) i + (√√5 sin þ sin 0)j + (√5 cos $) k, 0≤þ≤ñ/2, 0≤0≤2 The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using as needed.)
The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y, (1 — z)²). (b) Evaluate the integral JS.A demonstrating clearly how you derive the surface element ds. A.ds,
2
For the vector field G = (yey + 4 cos(4x + y))i + (xeªy + cos(4x + y)) ♬ find the line integral of G along the curve C from the origin along the x-axis to the point (4,0) and then counterclockwise around the circumference of the circle x² + y² = 16 to the point (4/√√2,4/√√2). ScĞ·dr = 0 }
(2) Let F(r, y, z) = yei- rzj+ cos zk. Compute curl F.
The last attempt was wrong could you please redo it. Thanks!
Find the scalar potential for the conservative field: F(x, y, z) = 12xyi + (6x² − 6z²)j + (−12zy +9)k The scalar potential is $(x, y, z) = ¯ +C Use this fact to evaluate Jo curve joining the points P = (3,3,0) and Q = (0, -3, -4). [B C F. dr = 0 F. dr where C is a smooth
7. Find the outward flux of the field F(x, y) = -yi + x² j across the closed counter-clockwise curve consisting of the top semi-circle of + y? = 4 followed by the straight line from (-2,0) to (2,0).
Let F(x, y, z) = 4xy²i + 2x²yzj — 3yz²k. Find div(F) and curl(F).
Calculate the áux of the field F(x, y) = (x - y)i + xj across the circley2+x2 = 1 in the xy-plane.
The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y, (1 z)²). Evaluate the integral JA demonstrating clearly how you derive the surface element ds. A.dS,

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