# Thread: Changing order of triple integral?

2. ## Re: Changing order of triple integral?

Start by draw a graph of the region of integration. The given integral has x going from 0 to 1, y going from 0 to 1, and z going from 0 to y- x. z= 0 is the xy-plane and z= y- x is also a plane that cuts the xy-plane in the line y= x. In the region 0<x< 1, 0< y< 1, that will be above the xy-plane for y> x and below it for y< x.

In (1.) the the last, "outside", integral is with respect to dy and must have numbers as limits. What are the smallest and largest values y can take on?
The second, "middle", integral is with respect to x. For each y, what are the smallest and largest values of x (as a function of y)?
The third, "inner", integral is with respect to z. For each x and y, what are the smallest and largest values of z (as a function of x and y)?

In (2.) the the last, "outside", integral is with respect to dz and must have numbers as limits. What are the smallest and largest values z can take on?
The second, "middle", integral is with respect to x. For each z, what are the smallest and largest values of x (as a function of z)?
The third, "inner", integral is with respect to y. For each x and z, what are the smallest and largest values of y (as a function of x and z)?