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Thread: Double Integral Over General Regions Problem

  1. #1
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    Double Integral Over General Regions Problem

    I am not sure what to do here

    Find the volume of the solid bounded by the cylinder x^2 + y^2 = 1 and the planes y = z, x = 0, z = 0 in the first octant.

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by machi4velli View Post
    I am not sure what to do here

    Find the volume of the solid bounded by the cylinder x^2 + y^2 = 1 and the planes y = z, x = 0, z = 0 in the first octant.

    Any help would be appreciated.
    The region is defined by (if I have done this correctly):

    Consider the point $\displaystyle (x,y)$ with $\displaystyle x^2+y^2<1$ in the first quadrant, then the height of the surface of the solid above this point is $\displaystyle y$ and all points from $\displaystyle (x,y,0)$ to $\displaystyle (x,y,y)$ are in the solid, so the required volume is:

    $\displaystyle
    V=\int_{x=0}^1 \int_{y=0}^{\sqrt{1-x^2}} y~dy~dx
    $

    RonL
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