Let S be the surface given by z = 1 − x² - y² above the region in the xy-plane given by 0 ≤ x ≤1 and 0 ≤ y ≤ 1 with upwards orientation. Which of the following integrals represents the flux of F(x, y, z) = (x, y, 1) through S. 1 So'² So² (x + y + 1 ) √ 1 + 4x² + 4y² dxdy ²² (2x² + 2y² + 1) dxdy √ (1 – 2x² - 2y²) dady 0 None of the above. V

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let S be the surface given by z = 1 − x² - y² above the region in the xy-plane given by 0 ≤
x ≤1 and 0 ≤ y ≤ 1 with upwards orientation. Which of the following integrals represents the
flux of F(x, y, z) = (x, y, 1) through S.
1
So'² So² (x + y + 1 ) √ 1 + 4x² + 4y² dxdy
²² (2x² + 2y² + 1) dxdy
√ (1 – 2x² - 2y²) dady
0
None of the above.
V
Transcribed Image Text:Let S be the surface given by z = 1 − x² - y² above the region in the xy-plane given by 0 ≤ x ≤1 and 0 ≤ y ≤ 1 with upwards orientation. Which of the following integrals represents the flux of F(x, y, z) = (x, y, 1) through S. 1 So'² So² (x + y + 1 ) √ 1 + 4x² + 4y² dxdy ²² (2x² + 2y² + 1) dxdy √ (1 – 2x² - 2y²) dady 0 None of the above. V
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