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Unformatted text preview: [(4 / 3) π ] / 16 = π/ 12 . (b) The required integral is Z π/ 2 φ =0 Z π/ 4 θ =0 Z 1 ρ =0 f ( ρ sin φ cos θ,ρ sin φ sin θ,ρ cos φ ) ρ 2 sin φdρdθ dφ by the change of variables formula. 2 (c) Notice that div F = 4, so that by the divergence theorem, ZZ S F · d S = ZZZ W div F dxdy dz = ZZZ W 4 dxdy dz = 4 × vol( W ) = π/ 3 using part (a)....
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