
Mass Triple Integrals
Find the mass of the solid region bounded by the planes
x+z=1
xz = 1
y=0
and the surface
y=sqrt(z)
The density of the solid is (x,y,z)=2y+5
My analytic geometry skills are a little lost. Could someone please remind me how to graph these planes so I can find the limits for my integrals?

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Hi. Use Mathematica to draw it. Oh I realize that's a lazy approach and cuts into your analytical education but if you're having problems visualizing it, then first get it (Mathematica), then figure out how the three equations give rise to the surfaces: Red is x+z=1, Blue is xz=1, and Green is y=Sqrt[z]. Now, in general, a triple integral is:
$\displaystyle \int_a^b\int_{y=f_1(x)}^{y=f_2(z)}\int_{z=g(x,y)}^ {z=h(x,y)} u(x,y,z) dzdydx$
so that's up from the surface g to the surface h, bordered in the xy plane between the functions f1 and f2, and then finally in the range of x from a to b.
So we want that teepee volume in there right and it's symmetrical to the zx plane since u=2y+5 so take half and multiply by two. So we go up from z=y^2 to the red sheet z=1x and the footprint in the xy plane is when the two equations y=Sqrt[z] and x+1=z are satisfied (the red and green surfaces intersect or x=y^21. So integrating in the order dzdxdy, I get:
$\displaystyle 2\int_0^1\int_0^{y^21}\int_{y^2}^{1x} (2y+5)dzdxdy$
but I'm not sure about it so you go over it and see if I missed it.