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Double integral, find volume of solid

  1. Oct 29, 2016 #1
    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:

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

    01x2-11-x2 5x+6y+18 dy dx


    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. jcsd
  3. Oct 29, 2016 #2


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    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?
  4. Oct 29, 2016 #3
    Yes, it's correct.
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