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Homework Help: Compute the volume of the solid

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Computer the volume of the solid bounded by the xz plane, the yz plane, the xy plane, the planes x = 1 and y = 1, and the surface z = x2 + y2

    2. Relevant equations


    3. The attempt at a solution

    Since the solid is bounded by the xz plane, the yz plane, the xy plane, it is assumed that the values of x, y, and z all equal 0. And since x = 1 and y = 1, the limits of integration is:

    0 [tex]\leq[/tex] x [tex]\leq[/tex] 1

    0 [tex]\leq[/tex] y [tex]\leq[/tex] 1

    Thus, the double integral is:

    [tex]\int[/tex] [tex]\int[/tex] x2 + y4 dA

    and the limits of integration is 0 [tex]\leq[/tex] x [tex]\leq[/tex] 1, 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1.

    After calculating the integral, I got the answer [tex]\frac{8}{15}[/tex]. Can anyone verify my work?
  2. jcsd
  3. Sep 28, 2010 #2


    Staff: Mentor

    That's what I get, too.

    For future reference, here is the integral I evaluated, using LaTeX.
    [tex]\int_{x = 0}^1 \int_{y = 0}^1 x^2 + y^4~dy~dx[/tex]

    Click the integral to see my LaTeX code.
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