Labware - MA35 Multivariable Calculus - Three Variable Calculus



Change of Order of Integration


Applied to continuous functions of three variables, Fubini's Theorem says that there are six different ways to evaluate integrals.

For a function f(x, y, z) with domain R such that a ≤ x ≤ b, c ≤ y ≤ d, k ≤ z ≤ l,

abcdklf(x, y, z)dzdydx =

abklcdf(x, y, z)dydzdx =

cdabklf(x, y, z)dzdxdy =

cdklabf(x, y, z)dxdzdy =

klabcdf(x, y, z)dydxdz =

klcdabf(x, y, z)dxdydz =

∫∫∫Rf(x, y, z)dV



  • In the 2-variable lab on Change of Order of Integration, there is a demo called "Slab Approximations." What would be the equivalent of a slab for integrals over three variables?