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Math Help - Volume using cross section

  1. #1
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    Volume using cross section

    Problem is "The base of a solid is the parabolic region {(x,y)|Y^2<=x<=1} OR from what I can tell x=Y^2 0<=x<=1 ( Answer is 2 )

    This means I have a simple base*height problem, it should be the integral from a to b of the area of these squares.

    But then I go to set up my integral and I get lost. I know I should have y^2 in there, but what goes with it?

    Thanks!

    ( Edit: How did my entire post cut off? )
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  2. #2
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    Quote Originally Posted by Wolvenmoon View Post
    Problem is "The base of a solid is the parabolic region {(x,y)|Y^2<=x<=1} OR from what I can tell x=Y^2 0<=x<=1 ( Answer is 2 )

    This means I have a simple base*height problem, it should be the integral from a to b of the area of these squares.

    But then I go to set up my integral and I get lost. I know I should have y^2 in there, but what goes with it?

    Thanks!

    ( Edit: How did my entire post cut off? )
    assuming the cross-sections are squares perpendicular to the x-axis ...

    x = y^2 ... y = \pm \sqrt{x}

    \displaystyle V = \int_0^1 (2\sqrt{x})^2 \, dx
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  3. #3
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    Thanks! ( I miss that but get fluid force on a dam right. LOL )
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