Question

Evaluate the flux of the vector field F = <3x, x^2 + y, e^(xy) - 2z> across the surface of the closed cylinder which can be expressed as a union of two surfaces A and B. Surface A is given by A = {(x, y, z) | x^2 + z^2 = 9, -5 ≤ y ≤ 5}, and surface B is given by B = {(x, y, z) | x^2 + y^2 ≤ 9, y = ±5}.

Name: evaluate the flux of the vector field f 3x x2 y exy 2z across the surface of the closed cylinder which can be expressed as a union of two surfaces a and b which is given by a x y zx2 z2 9 5 99526
Uploaded: 2023-01-06T09:46:02-08:00
Duration: 3 min 32 s
Channel: Madhur L
Description: evaluate the flux of the vector field f 3x x2 y exy 2z across the surface of the closed cylinder which can be expressed as a union of two surfaces a and b which is given by a x y zx2 z2 9 5 99526

          Evaluate the flux of the vector field F = <3x, x^2 + y, e^(xy) - 2z> across the surface of the closed cylinder which can be expressed as a union of two surfaces A and B. Surface A is given by A = {(x, y, z) | x^2 + z^2 = 9, -5 ≤ y ≤ 5}, and surface B is given by B = {(x, y, z) | x^2 + y^2 ≤ 9, y = ±5}.

Added by Shane S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

01/06/2023

Step 1

For surface A, we have a cylinder with radius 3 and height 10. The outward normal vector on the surface of the cylinder is given by <x, 0, z>. So, the flux across A is given by the surface integral of F dot n dS, where n is the outward normal vector and dS is the Show more…

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Evaluate the flux of the vector field F = <3x, x^2 + y, e^(xy) - 2z> across the surface of the closed cylinder which can be expressed as a union of two surfaces A and B. Surface A is given by A = {(x, y, z) | x^2 + z^2 = 9, -5 ≤ y ≤ 5}, and surface B is given by B = {(x, y, z) | x^2 + y^2 ≤ 9, y = ±5}.