So I have this surfaces $xy=1,xy=9,xz=4,xz=36,yz=25,yz=49$ But I could not identify the region so I tried transforming it.$$u=xy\quad\quad v=xz \quad\quad w=yz$$ which turns them into planes.
But now I am confused on how to use the partial derivatives jacobian.
The determinant of the matrix $\frac{\delta(x,y,z)}{\delta(u,v,w)} $ led me to $-2xyz$ but now how can I find the integral in this $uvw$ coordinates? $$\int_{25}^{49}\int_4^{36}\int_1^9 dudvdw$$ But I know I have to use in that integral somenthing related to the Jacobian, not sure what
You can use $uvw=x^2y^2z^2$. If your $x$, $y$, and $z$ are positive, just take the square root