An other place that determinant is applied is in the change of variable formula for integrals over regions in . We restrict ourselves to integrals over regions in
.
Let be a region in
-plane and
be a region in
-plane. Let
and
be related by the equations
and
such that every pont in
is the image of a unique point in
. Let
be a continuous function on
. Assume that
and
have continuous partial derivatives on
. Also assume that
. It can be shown that