Section 15.9: Change of Variables in Multiple Integrals

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes. R is bounded by the hyperbolas \(y=1/x, y=4/x\) and the lines \(y=x, y=4x\) in the first quadrant.