# Change of variables (i don,t understand)

eljose
let be the integral:

$$\int_1^{\infty}\int_{-\infty}^{\infty}f(x,y)dydx$$

i make the change of variable xy=u y=v whose Jacobian is 1/v but then what would be the new limits?...

Homework Helper
eljose said:
let be the integral:

$$\int_1^{\infty}\int_{-\infty}^{\infty}f(x,y)dydx$$

i make the change of variable xy=u y=v whose Jacobian is 1/v but then what would be the new limits?...

v is y, so u = xv, and x can never be less than 1. What does that tell you about the possible values of u for any given v?

eljose
could you write the new limits...i can,t work it out the new values of v for v gives me (-8,8) (here 8 means infinite but for u i got... (0,8) is that true?..what would happen if y choose the change of variable x/y=u y=v? thanx

Homework Helper
eljose said:
could you write the new limits...i can,t work it out the new values of v for v gives me (-8,8) (here 8 means infinite but for u i got... (0,8) is that true?..
$$\int_1^{\infty}\int_{-\infty}^{\infty}f(x,y)dydx$$
$$\int_{-\infty}^{0}\int_{-\infty}^{v}g(u,v)dudv + \int_{0}^{\infty}\int_v^{\infty}g(u,v)dudv$$