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# 11.04 - Section 12.7 Spherical coordinates Main ideas...

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Section 12.7: Spherical coordinates Main ideas? ..?.. Spherical coordinates: ( x , y , z ) Cartesian = ( ρ , θ , φ ) polar , where x = ρ sin φ cos θ , y = ρ sin φ sin θ , z = ρ cos φ . with ρ 0, 0 θ 2 π , 0 φ π . Triple integrals can be easier to evaluate in spherical coordinates if the domain of integration has spherical symmetry, and/or the integrand has spherical symmetry. If E = {( ρ , θ , φ ) spherical : a ρ b , α θ β , c φ d }, then ∫∫ ∫ E f ( x , y , z ) dV = … ..?.. a b α β c d f ( ρ sin φ cos θ , ρ sin φ sin θ , ρ cos φ ) ρ 2 sin φ d φ d θ d ρ . (Stewart writes it differently: he writes

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11.04 - Section 12.7 Spherical coordinates Main ideas...

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