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Math Help - Volumes by Rotation

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    Volumes by Rotation

    Find the volume of the solid that results when the region enclosed by x=y^2, and x=y is revolved about the line x=-1.
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    Quote Originally Posted by kinana18 View Post
    Find the volume of the solid that results when the region enclosed by x=y^2, and x=y is revolved about the line x=-1
    most important ... sketch a diagram.

    x = y^2 and x = y intersect at y = 0 and y = 1

    washers w/r to y ...

    V = \pi \int_c^d [R(y)]^2 - [r(y)]^2 \, dy

    R(y) = y - (-1) = y + 1

    r(y) = y^2 - (-1) = y^2 + 1

    V = \pi \int_0^1 (y+1)^2 - (y^2+1)^2 \, dy
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