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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 -

    find their intersection
    x^2 - 6x + 10 = x
    x = 2 or x = 5

    volume = π [integral](x^2 - (x^2 - 6x + 10)^2 dx from 2 to 5

    I would expand (x^2 - 6x + 10)^2
    after that it just becomes a routine integration of simple terms and careful arithmetic.

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