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Math Help - Volume of solid

  1. #1
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    Volume of solid

    Dear Folks,

    The base of the volume is the region between two parabolas.
    Find the volume of the solid given that cross-sections perpendicular to the x-axis are squares.

    Give Hints please.
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  2. #2
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    Re: Volume of solid

    Quote Originally Posted by Simplictic View Post
    Dear Folks,

    The base of the volume is the region between two parabolas.
    Find the volume of the solid given that cross-sections perpendicular to the x-axis are squares.

    Give Hints please.
    V = \int_a^b [f(x) - g(x)]^2 \, dx

    where x = a and x = b are the x-coordinates of the parabolas intersection points

    f(x) = upper parabola

    g(x) = lower parabola

    in future, please place questions that involve integration in the calculus forum.
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  3. #3
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    Re: Volume of solid

    Quote Originally Posted by skeeter View Post
    V = \int_a^b [f(x) - g(x)]^2 \, dx

    where x = a and x = b are the x-coordinates of the parabolas intersection points

    f(x) = upper parabola

    g(x) = lower parabola

    in future, please place questions that involve integration in the calculus forum.
    Thanks skeeter,

    If parabolas are  x = y^{2} and x = 3 -y^{2}, is it reasonable to make y subject to have y= f(x), y = g(x) or we need to use x = f(y) in the formula for volume?
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  4. #4
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    Re: Volume of solid

    Quote Originally Posted by Simplictic View Post
    Thanks skeeter,

    If parabolas are  x = y^{2} and x = 3 -y^{2}, is it reasonable to make y subject to have y= f(x), y = g(x) or we need to use x = f(y) in the formula for volume?
    are the cross-sections still perpendicular to the x-axis?
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