Labware - MA35 Multivariable Calculus - Two Variable Calculus

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Change of Order of Integration (Page: 1 | 2 )

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If we apply Fubini's Theorem to integrals using polar coordinates, we get

abcdf(x, y)rdrdθ = ∫cdabf(x, y)rdθdr = ∫∫Rf(r, θ)dA

Where dA = dr*dθ.

Demos

Exercises

  • One of the change of order of integration demos for Cartesian coordinates discusses "slab approximations". What would slabs look like in polar coordinates? How would you use summation and integral notation to describe slab approximations in polar coordinates?