Josephood7

Use the change of variables [math], [math] to compute [math], where [math] is the region bounded by [math].

[math] 

Let [math]. Use the Jacobian to determine the area of [math] for:

[math]

[math]

[math] 

[math] 

 In this problem we use the change of variables [math], [math] to compute the integral [math], where [math] is the parallelogram with vertices [math], [math], [math], and [math].

First find the magnitude of the Jacobian, [math]  .

Then, with [math]  , [math]  ,
[math]  , and [math]  ,
[math]  [math]  [math]  [math] = 

Show that [math] maps the triangle [math] to the domain [math] bounded by [math], [math],
and [math]. Use [math] to evaluate [math] Answer :