Changing Order of Integration for Multiple Integrals Click here for 2-D Example

 1 In a Nut Shell:  The evaluation of double or triple integrals over a region, R, may be complicated due to the complexity of the integrand, due to the order of integration, or both.  The strategy is the same for both double and triple integrals but the triple integrals are generally harder since you are dealing with intersecting surfaces that are harder to visualize rather than intersecting curves.   The strategy is to identify the surfaces (or curves) that bound the region of integration, by drawing the projections of the surfaces on various planes.  In so doing you will identify the limits of integration in each plane.  Then pick an order of integration that simplifies evaluation of the integral. 2 Example:   Change the order of integration for the integral below from  dy dz dx to  dx dz dy.                        x = 1   z = 1-x2   y = 1 - x            I    =     ∫           ∫            ∫       f(x,y,z)  dy dz dx                       x = 0   z = 0       y = 0   The first step is to visualize, R, the region of integration and the intersecting surfaces by examining the given limits of integration.                        Click here to continue with this example.