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
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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 12E
Question
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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