Calculate the line integral of the vector field F = (5xy, x, y + z) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is given by z = 1x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [₁ F. dr = curl(F) = Ic curl(F). ds =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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17.2 #1

Calculate the line integral of the vector field F
=
: (5xy, x, y + z) around the boundary curve, the curl of the vector field, and the
surface integral of the curl of the vector field.
The surface S is given by
z = 1 - x² - y² for x² + y² ≤ 1
oriented with an upward-pointing normal.
(Use symbolic notation and fractions where needed.)
F. dr =
curl(F) =
D
curl(F). dS =
Transcribed Image Text:Calculate the line integral of the vector field F = : (5xy, x, y + z) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is given by z = 1 - x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) F. dr = curl(F) = D curl(F). dS =
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