Triple Integral (Type 1 Solid Region)

 

 

Example:  Determine the limits of integration using a Type 1 Solid region for the

triple integral   

                                 I   =  ∫  ∫  ∫  [ f dz ]  dA where  the region (shown below) is

 

bounded by the plane  z = 1 – y,  the surface y = √ x, the yz-plane and the xy-plane. 

 

 

 

The first integration for Type 1 Solid regions is in the z-direction.  In this example,

start by “sweeping” the element of volume, dz dA from z = 0 to z = 1 – y.

 

               

                                  

 

 

 

To determine the limits of integration in the x and y directions, project the solid region

on to the xy-plane and examine the intersections.  The order of integration for

x and y is optional.  See the figures below.

 

 

                       

 

Click here to continue with this example.

 



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