# change of variables for 3 dimensional integral

Let $\int_{0}^{\infty}\int_{0}^{\infty}\int_{-\infty}^{\infty}f(x_1,x_2,x_3)dx_1dx_2dx_3$ be a 3 dimensional integral ( thus $0\leq x_1\leq \infty, 0\leq x_2\leq \infty,-\infty\leq x_3\leq \infty$) Define a change of variable : $x_1'=x_1,x_2'=x_2$ and $$x_3'=c_1x_1+c_2x_2+c_3x_3$$

What are the new boundaries of the integral in $x_1',x_2',x_3'$ after this change of variable? I understand the Jacobian concept but have difficulties to find the boundary. Any help with explanation of how to find these generally is appreciated.

Thanks

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Same question as here. –  David Moews Mar 1 '13 at 23:39