Chapter 14.7, Problem 3QCE

Let T be the transformation in Quick Check Exercise 1.

(a) The Jacobian $\partial \left(x,y\right)/\partial \left(u,\upsilon \right)$ of T is $\text{\_\_\_\_\_\_}\text{.}$

(b) Let R be the region in Quick Check Exercise 1(a). Fill in the missing integrand and limits of integration for the change of variables given by T.

${\displaystyle \underset{R}{\iint }{e}^{x+2y}dA}={\displaystyle {\int }_{\boxed{}}^{\boxed{}}{\displaystyle {\int }_{\boxed{}}^{\boxed{}}\text{\_\_\_\_\_}dud\upsilon }}$