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Math Help - Triple Integration

  1. #1
    Newbie sherryl's Avatar
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    Triple Integration

    Find volume of solid region in first octant by triple integration:

    Solid is bounded by elliptic cylinder 2x+y=1 and the plane y+z=1


    So far I've gotten to:

    \int\nolimits_{0}^{\frac{1}{\sqrt {2} }} {dx}\int\nolimits_{0}^{\sqrt {1-2x^{2}} } {dy}\int\nolimits_{0}^{1-y} {dz}

    Is this on the right track?
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  2. #2
    A Plied Mathematician
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    Looks good so far. To avoid confusion, I would probably write the integral as

    \int_{0}^{\frac{1}{\sqrt {2} }} \int_{0}^{\sqrt {1-2x^{2}} } \int_{0}^{1-y} dz\,dy\,dx.
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