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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
(1 point) Let S be the cube with side length 2, faces parallel to the coordinate planes, and centered at the origin.
(a) Calculate the total flux of the constant vector field = 5 i+2j - 5k out of S by computing the flux through each face separately.
flux through the face at x = 1:
flux through the face at y = 1:
flux through the face at x = 1:
flux through the face at x = -1:
flux through the face at y = -1:
flux through the face at x = -1:
Thus the total flux is
flux=
Calculate the flux out of S for any constant vector field = ai + bj+ck.
flux =
(Be sure that you can explain why your answers to parts (a) and (b) make sense.)
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