Labware - MA35 Multivariable Calculus - Two Variable Calculus

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

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Fubini's Theorem states that for a continuous function of x and y with a rectangular domain, one can evaluate a double integral by first integrating with respect to x (treating y as a constant) and then integrating this result with respect to y (treating x as a constant), or by first integrating with respect to y (treating x as a constant) and then integrating this result with respect to x (treating y as a constant).

Formally, for a function f(x, y) with domain R such that a ≤ x ≤ b, c ≤ y ≤ d,

abcdf(x, y)dydx = ∫cdabf(x, y)dxdy = ∫∫Rf(x, y)dA

Demos

Exercises

  • The "Slab Approximations" demo description mentions that the series of slabs represents the summation of an integral. Would it be possible instead to take the integral of a summation and get the same result? Compare and contrast these two processes.