Chapter 13, Problem 74RE

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.

74.     ${\displaystyle \underset{R}{\iint }3x{y}^{2}dA;R=\left\{\left(x,y\right):0\le x\le 2,x\le y\le x+4\right\}}$ use x = 2u, y = 4v + 2u