Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi-yj+z3k, S is the part of the cone z = x²+y2 between the planes z = 1 and z = 2 with downward orientation 15л ZA z=2

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Evaluate the surface integral
F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = -xi - yj + z³k, S is the part of the cone z =
x² +
between the planes z = 1 and z = 2 with downward orientation
ZA
z = √√x² + y²
15π
×
x
-z=2
z=1
Transcribed Image Text:Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi - yj + z³k, S is the part of the cone z = x² + between the planes z = 1 and z = 2 with downward orientation ZA z = √√x² + y² 15π × x -z=2 z=1
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