Let S S be the upper hemisphere x 2 + y 2 + z 2 = 1
Question:
Let S be the upper hemisphere x2+y2+z2=1,z≥0. For each of the functions (a)-(d), determine whether \(\iint_{\mathcal{S}} f d S\) is positive, zero, or negative (without evaluating the integral). Explain your reasoning.
(a) \(f(x, y, z)=y^{3}\)
(b) \(f(x, y, z)=z^{3}\)
(c) \(f(x, y, z)=x y z\)
(d) \(f(x, y, z)=z^{2}-2\)
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a Since fx y zy3 is an odd function of y and the upper hemisphere i...View the full answer
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