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Thread: Triple Integrals In Cylindrical Coordinates.

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    Triple Integrals In Cylindrical Coordinates.

    Using cylindrical coordinates, evaluate (OVER R) $\displaystyle \int \int \int \sqrt{x^2+y^2} dV$ , where the solid R is bounded by the surfaces $\displaystyle z=\sqrt{x^2+y^2}$ and z=5.

    OK, I know how to graph these two surfaces, But how in the earth can I find the limits of the integration?
    the "$\displaystyle dz$" limits: $\displaystyle 5 \rightarrow r$
    but what about "$\displaystyle d\theta$" and "$\displaystyle dr$" ??!
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    Quote Originally Posted by TWiX View Post
    Using cylindrical coordinates, evaluate (OVER R) $\displaystyle \int \int \int \sqrt{x^2+y^2} dV$ , where the solid R is bounded by the surfaces $\displaystyle z=\sqrt{x^2+y^2}$ and z=5.

    OK, I know how to graph these two surfaces, But how in the earth can I find the limits of the integration?
    the "$\displaystyle dz$" limits: $\displaystyle 5 \rightarrow r$
    but what about "$\displaystyle d\theta$" and "$\displaystyle dr$" ??!
    the inside integral $\displaystyle \int_r^5 ( \cdot) dz$

    The two surfaces intersect giving a circle of radius 5. This is the region for the outer two integrals.
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    Quote Originally Posted by Danny View Post
    the inside integral $\displaystyle \int_r^5 ( \cdot) dz$

    The two surfaces intersect giving a circle of radius 5. This is the region for the outer two integrals.
    Nyahahahaa
    I got it
    But there is a little problem
    why is it from r to 5 ?
    why not from 5 to r ?
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    Quote Originally Posted by TWiX View Post
    Nyahahahaa
    I got it
    But there is a little problem
    why is it from r to 5 ?
    why not from 5 to r ?
    The cone ($\displaystyle z=r$) is below the plane ($\displaystyle z=5$).
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    Quote Originally Posted by Danny View Post
    The cone ($\displaystyle z=r$) is below the plane ($\displaystyle z=5$).
    hmmmm
    I did not memorize the shapes
    THANK YOU
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    Quote Originally Posted by TWiX View Post
    Nyahahahaa
    I got it
    But there is a little problem
    why is it from r to 5 ?
    why not from 5 to r ?
    Quote Originally Posted by TWiX View Post
    hmmmm
    I did not memorize the shapes
    THANK YOU
    Well, you don't have to memorize the shapes. At (0,0), z= 0 for the cone and z= 5 for the plane. 5> 0.

    Also it is neither "from r to 5" nor "from 5 to r". It is "r ranges from 0 to 5".
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