Chapter 13, Problem 76RE

Double integrals—transformation given To evaluate the following integrals, carry out the following steps.

a.    Sketch the original region of integration R and the new region S using the given change of variables.

b.    Find the limits of integration for the new integral with respect to u and v.

c.    Compute the Jacobian.

d.    Chance variables and evaluate the new integral.

76.     ${\displaystyle \underset{R}{\iint }x{y}^{2}dA;}$ R is the region between the hyperbolas xy = 1 and xy = 4 and the lines y = 1 and y = 4; use x = u/v, y = v.