Double integral to find volume of a solid

[mikky05v]

Homework Statement
Set up a double integral to find the volume of the solid bounded by the graphs y=4-x² and z=4-x²


The attempt at a solution

I drew myself a 3d graph but it's just a parabloid in the xy plane and a parabloid in the xz plane right? so I'm unsure how to set up my integral. This was my attempt, my thought was that perhaps z=4-x² could be considered like the surface

[itex]\int[/itex]²₀[itex]\int[/itex]^4-x2₀ (4-x²) dy dx

Could some one give me some input?

 

[LCKurtz]

Homework Statement
Set up a double integral to find the volume of the solid bounded by the graphs y=4-x² and z=4-x²


The attempt at a solution

I drew myself a 3d graph but it's just a parabloid in the xy plane and a parabloid in the xz plane right? so I'm unsure how to set up my integral. This was my attempt, my thought was that perhaps z=4-x² could be considered like the surface

[itex]\int[/itex]²₀[itex]\int[/itex]^4-x2₀ (4-x²) dy dx

Could some one give me some input?

What you have done looks reasonable, but isn't there more detail about the region in question? Like first octant or y positive or something?? Otherwise the volume isn't bounded. Can't tell if your answer is correct without knowing more.

 

[mikky05v]

oh yes sorry first octant is what it says. I wasn't entirely sure what that meant but I assumed it meant only the positive section of the 3d graph

 

[LCKurtz]

oh yes sorry first octant is what it says. I wasn't entirely sure what that meant but I assumed it meant only the positive section of the 3d graph

The first octant is where all three variables are positive. If that's your region your integral is set up correctly.