Double integral, find volume of solid

[ooohffff]

Homework Statement

Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders:
y = 1 − x²,
y = x² − 1
and the planes:
x + y + z = 2
4x + 5y − z + 20 = 0

Homework Equations

∫∫f(x,y) dA

The Attempt at a Solution

So I solved for z in the plane equations:
z=2-x-y
z=4x+5y+20

I subtracted these two equations:
(4x+5y+20)-(2-x-y) = 5x+6y+18 = z

∫₀¹ ∫_x²-1^1-x2 5x+6y+18 dy dx

=53/2

It's the wrong answer, and I think my x boundaries might be between -1 and 1 after graphing it but I'm not sure.

 

[LCKurtz]

If you graph $y=1-x^2$ and $y=x^2-1$ in the xy plane that should settle the $x$ limits for you. If you use $x=-1$ for the lower limit, does that fix it for you?

 

[ooohffff]

If you graph $y=1-x^2$ and $y=x^2-1$ in the xy plane that should settle the $x$ limits for you. If you use $x=-1$ for the lower limit, does that fix it for you?

Yes, it's correct.