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Find the area of the shaded region.


View the graph and image at:

postimg.o rg/image/dg4kt89v1/

Please help me explain this one. I know the ans to this one but can not work out.

  • math -

    you have to do in in two parts
    we need the x-intercept:
    0 = √x-3
    √x = 3
    x = 9

    area from 0 to 9 + area from 9 to 16
    (If you do it in one calculation from 0 to 16, the area which is below the x-axis will work its way into the answer as a negative area)


    y = √x - 3
    Area = ∫(-x^(1/2) + 3) dx from 0 to 9 + ∫(x^(1/2) - 3) dx from 9 to 16
    = (-(2/3)x^(3/2) + 3x)|from 0 to 9 + ((2/3)x^(3/2) - 3x)| from 9 to 16
    =(-2/3)(27) + 27 - 0 + (2/3)(64) - 48 - ((2/3)(27) - 27)
    = -18 + 27 + 128/3 - 48 - 18 + 27
    = 38/3

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