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) = xy i + yz j + zx k S is the part of the paraboloid z = 4 - x2 - y² that lies above the square 0sxs 1,0 s y s 1, and has upward orientation

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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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) = xy i + yz j + zx k
S is the part of the paraboloid z = 4 - x2 - y2 that lies above the square 0 < x < 1, 0 sys 1, and has upward orientation
823
180
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) = xy i + yz j + zx k S is the part of the paraboloid z = 4 - x2 - y2 that lies above the square 0 < x < 1, 0 sys 1, and has upward orientation 823 180
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