# Double integral, find volume of solid

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1. Oct 29, 2016

### ooohffff

1. The problem statement, all variables and given/known data
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

2. Relevant equations
∫∫f(x,y) dA

3. 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

01x2-11-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.

2. Oct 29, 2016

### 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?

3. Oct 29, 2016

### ooohffff

Yes, it's correct.