Question

Suggestions for integral variable change? http://tinypic.com/r/2s7xboj/8

Answer 1

you don't need a variable change:$$e^{2x+3y}=e^{2x}e^{3y}$$recall \(\int\int f(x)g(y)\,dy\,dx=\int f\,dx\cdot\int g\,dy\)

Answer 2

variable change might simplify the bounds ?

Answer 3

the bound as it exists is already pretty simple; the only change of variables worthwhile is straightforward \((u,v)=(2x,3y)\)

Answer 4

from a rhombus to a rectangle maybe.. not sure

Answer 5

if you feel the need :-p

Answer 6

yeah the region is already simple, not worth of a variable change i see :)

Answer 7

ok, thx

Answer 8

its just that i wanted to avoid doing 4 integrals

Answer 9

two integrals will do

Answer 10

if you want to avoid doing 2 integrals, try the change change of variables suggested by oldrin.bataku and find the jacobian : \(\large dudv = \left|\begin{matrix}u_x&u_y\\v_x&v_y\end{matrix}\right|dxdy\)