Compute the area of the region D bounded by xy=1, xy=16, xy2=1, xy2=36 in the first quadrant of the xy-plane. Using the non-linear change of variables u=xy and v=xy2, find x and y as functions of u and v.
x=x(u, v)= ?
y=y(u, v)=?
Find the determinant of the Jacobian for this change of variables.
∣∣∣∂(x, y)/∂(u, v)∣∣∣=det=?
Using the change of variables, set up a double integral for calculating the area of the region D.
∫∫Ddxdy=?
Evaluate the double integral and compute the area of the region D.
Area =