Problem solving this volume using Jacobi's Determinant

[JorgeM]

Homework Statement

Find the value of the solid's volume given by the ecuation 3x+4y+2z=10 as ceiling,and the cilindric surfaces
2x^2=y
x^2=3*y
4y^2=x
y^2=3x
and the xy plane as floor.

The Attempt at a Solution

I know that we have to give the ecuation this form:
∫∫z(x,y)dxdy= Volume
So, in fact we have to solve:
∫∫ ( 3 - 1.5x - .5y ) dxdy but actually it is easier to do variables' change because of the fact that the limits are to tricky to solve.

I get so confused when I try to suppose a good change and use in the Jacobi's determinant.
Hope you could help my because I got so confused :(

Thanks for your advise.

 

[fresh_42]

Just to visualize your solid. On the (x,y) plane it looks like the grey area in

where the blue line is from the ceiling, a pyramid which crosses the z axis at 5 indicated by the pink area.

You can try to figure out your limits for the integrals with this picture in mind.