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Math Help - Need help setting this integral.

  1. #1
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    Need help setting this integral.

    Solid bounded above by z=2-x^2-y^2 and below by z=x^2+y^2.
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  2. #2
    MHF Contributor Amer's Avatar
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    \int\int\int_S dzdydx

    Need help setting this integral.-graph.jpg

    z_1 = 2-x^2 -y^2 , z_2 = x^2 +y^2

    z_1 = z_2

    2-x^2 -y^2 = x^2 +y^2 \Rightarrow x^2 +y^2 =1

    z change from z_2 to z_1

    Need help setting this integral.-graoh2.jpg

    \int_{-1}^{1} \int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}} \int_{x^2+y^2}^{2-x^2-y^2} dz dx dy
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  3. #3
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    Can you do it in cylindrical coordinates?
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  4. #4
    MHF Contributor Amer's Avatar
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    \int_{0}^{2\pi}\int_{0}^{1}\int_{r^2}^{2-r^2} r dzdrd\theta
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