Given this integral $\int_0^1\int_0^{1-(y-1)^2}\int_0^{2-x}f(x,y,z)dzdxdy$ , how can I interchange the variables and express as integrals of the other five forms like dxdydz,dxdzdy...??
So what I have figured out is that it is a region bounded by z=0,z=2-x and x=1-$(y-1)^2$ ,0$\le$y$\le$1.
Can anyone explain one case to me? say dxdydz?
You will have to draw the region.Region in xy plane is bounded by $x=1-(y-1)^2 $ , a parabola and y=1. and from there z from 0 to z=x-2, a plane. Now if you project that volume on yz plane you will see its a rectangle bounded by z=2 and y=1, Now we can setup this integral, in order dxdydz
$$\int_0^2\int_0^{1}\int_0^{1-(y-1)^2}f(x,y,z)dxdydz$$