A farmer planted eight fields of vegetables. Of the fields planted 1/4 were planted with beans. How many fields of beans did the
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Under the given transformation, the Jacobian and its determinant are
so that
where is the region
transformed into the
-
plane. The remaining integral is the twice the area of
.
Now, the integral over is
but through the given transformation, the boundary of is the set of equations,
We require that , and the last equation tells us that we would also need
. This means
and
, so that the integral over
is