What is the volume enclosed by the parabolic cylinder and two planes?

[fishingspree2]

Homework Statement

Find the volume of the solid enclosed by the parabolic cylinder y=10 - a²x² and the planes z=y and z=2-y, where a > 0 is a constant.

Homework Equations

I have graphed the 3 surfaces on Maple to visualize the solid enclosed by these surfaces but the problem is there is no closed solid. There is not one single closed solid formed so I really don't know which volume we are looking for. Computing the volume of an unclosed solid would give me an infinite volume, which I am sure is not what the question asks. Can someone please help me?

using a =2

 

[lanedance]

i think maybe you have graphed z=10 - a^2y^2, rather than y=10 - a^2x^2

 

[lanedance]

then you will need to separate into 2 integrals, depending on which plane is the bound