(1 point) Compute the area of the region D bounded by
$\ xy = 1, xy = 4, xy^2 = 1, xy^2 = 36$
in the first quadrant of the $xy$-plane.
(a) Graph the region D.
(b) Using the non-linear change of variables $u = xy$ and $v = xy^2$, find $x$ and $y$ as functions of $u$ and $v$.
$x = x(u, v) = $
$y = y(u, v) = $
(c) Find the determinant of the Jacobian for this change of variables.
$\frac{\partial(x, y)}{\partial(u, v)} = det$
(d) Using the change of variables, set up a double integral for calculating the area of the region D.
$\iint_D dx\ dy = \int_a^b \int_c^d \frac{\partial(x, y)}{\partial(u, v)} du\ dv = $
(e) Evaluate the double integral and compute the area of the region D.
Area =
