Order of integration (calculus)

The difficulty with this interchange is determining the change in description of the domain D. The method also is applicable to other multiple integrals.

Reduction to a single integration makes a numerical evaluation much easier and more efficient.

This forms a three dimensional slice dx wide along the x-axis, from y=a to y=x along the y-axis, and in the z direction z=h(y).

For application to principal-value integrals, see Whittaker and Watson,[5] Gakhov,[6] Lu,[7] or Zwillinger.

[10] A discussion of the basis for reversing the order of integration is found in the book Fourier Analysis by T.W.

[12] He introduces his discussion with an example where interchange of integration leads to two different answers because the conditions of Theorem II below are not satisfied.

Figure 1: Integration over the triangular area can be done using vertical or horizontal strips as the first step. This is an overhead view, looking down the z -axis onto the xy -plane. The sloped line is the curve y = x .