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Math Help - Find volume of solid using squares

  1. #1
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    Find volume of solid using squares

    The base of a certain solid is a region in the first quadrant bounded by the curve and . Find the volume of the solid if each gross section perpendicular to the x-axis is a square with one edge in the base of the solid.


    Attempt to solution:

    A= s^2= (x-x^2)^2

    V=\int_0^1(x-x^2)^2


    How come the textbook has it the other way round


    V=\int_0^1(x^2-x)^2
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  2. #2
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    Does it matter? Not in this case.

    It is traditional to write things in decreasing exponents.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    I think what needs to be observed here is that x-x^2=-\left(x^2-x\right) but \left(x-x^2\right)^2=\left(-\left(x^2-x\right)\right)^2=(-1)^2\left(x^2-x\right)^2=\left(x^2-x\right)^2
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