Next: Centroids and Centers Up: Background Previous: Computing double integrals

Triple integrals

Computing triple integrals with Maple proceeds in a similar fashion. For example, the command to perform the following integral

is

```  > int(int(int(exp(x)*y*z^2,x=0..1),y=1..2),z=-1..1);
```

It is sometimes helpful when you aren't sure you have the command right to use the Int command, which is an inert form of the int command. Inert means that Maple just displays the integral and does not try to evaluate it. Here is an example.

```  > Int(Int(Int(exp(x)*y*z^2,x=0..1),y=1..2),z=-1..1);
```

By using the inert Int command, you can easily check that the limits and the order of integration are correct.

More complicated triple integrals can also be done. For example, the volume of the region bounded by the paraboloid and the plane z=y+2 is given by the triple integral

This integral can be computed with the following Maple command.

```  > int(int(int(1,x=-sqrt(z-y^2)..sqrt(z-y^2)),z=y^2..y+2),y=-1..2);
```

William W. Farr
Thu Apr 25 17:53:00 EDT 1996