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1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis?

  • math -

    First define the x limits of the enclosed region. They are between the two roots of
    x^2 -6x +10 = x
    x^2 -7x +10 = 0
    (x - 5)(x -2)= 0

    You want to integrate between x = 2 and 5.

    The function that you integrate is
    f(x) = pi*{-[x^2 -6x +10]^2 + x^2} dx.
    The y = x curve lies above the parabola in the interval

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