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Math Help - Double integrals into polar coordinates

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    Red face Double integrals into polar coordinates

    Use the double integral in polar coordinates to find the volume of the solid bounded by the graphs of the given equuations :

    z= x^2+y^2+3 , z=0 , x^2+y^2=1
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    Quote Originally Posted by cchyfly View Post
    Use the double integral in polar coordinates to find the volume of the solid bounded by the graphs of the given equuations :

    z= x^2+y^2+3 , z=0 , x^2+y^2=1
    \iint_Dx^2+y^2+3dA=\int_{0}^{2\pi}\int_{0}^{1}(r^2  +3)rdrd\theta

    \int_{0}^{2\pi}\left( \frac{1}{4}r^4+\frac{3}{2}r^2\right)|_{0}^{1}d\the  ta=\frac{7}{4}\int_{0}^{2\pi}d\theta=\frac{7\pi}{2  }
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    Hello TheEmptySet,

    I have a question to this (I'm trying to understand these problems) :
    Where did we use the fact that it was bounded by z=0 ?
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    Quote Originally Posted by Moo View Post
    Hello TheEmptySet,

    I have a question to this (I'm trying to understand these problems) :
    Where did we use the fact that it was bounded by z=0 ?
    The integrand x^2+y^2+3
    is the height above the xy plane. As we integrate over the area in the xy plane we get the volume between the surface and the plane z=0.

    The 2d equivelent is finding the area under the curve y=x^2 from x=2 to x=4. We use the fact that it is bounded below by y=0 to get the area between the curve and the x axis.

    I hope this Helps.

    Brett
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    Moo
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    Quote Originally Posted by TheEmptySet View Post
    The integrand x^2+y^2+3
    is the height above the xy plane. As we integrate over the area in the xy plane we get the volume between the surface and the plane z=0.

    The 2d equivelent is finding the area under the curve y=x^2 from x=2 to x=4. We use the fact that it is bounded below by y=0 to get the area between the curve and the x axis.

    I hope this Helps.

    Brett
    Ouh, thanks !
    It's (quite ) ok for the first part, but I don't see where x comes from in the second part ? And how do you get the boundaries 2 & 4 ?
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    Quote Originally Posted by Moo View Post
    Ouh, thanks !
    It's (quite ) ok for the first part, but I don't see where x comes from in the second part ? And how do you get the boundaries 2 & 4 ?

    O just made that up for the sake of an example. It is not related to the prevoius problem. Sorry.

    Brett
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