Triple Integrals in Cylindrical Coordinates
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6 Terms
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Cylindrical Coordinates
A coordinate system in three dimensions that is similar to polar coordinates and gives convenient descriptions of some commonly occurring surfaces and solids.
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Conversion from Cylindrical to Rectangular Coordinates
x = r cos θ, y = r sin θ, z = z
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Conversion from Rectangular to Cylindrical Coordinates
r^2 = x^2 + y^2, tan θ = y/x, z = z
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Graph of θ = c
A vertical plane through the origin.
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Graph of z = c
A horizontal plane.
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Triple Integral in Cylindrical Coordinates
∫∫∫E f(x, y, z) dV = ∫∫∫E f(r cos θ, r sin θ, z) r dz dr dθ