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Math Help - Calculate the area

  1. #1
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    Calculate the area

    Calculate the area of the region limited by curves:

    1) y=x^3 and y=x^2+2x

    answer: \frac{37}{12}

    2) y=x^3-2x^2-5x+6, the axis-x, x=-1 and x=2

    answer: \frac{157}{12}
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  2. #2
    Senior Member Spec's Avatar
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    1) Check where the two curves meet:

    x^3 = x^2 + 2x which gives three points: x=-1, x=0, x=2

    So you need to split the integration area up into two parts:

    \int_{-1}^0 (x^3 - (x^2 + 2x))dx + \int_0^2 (x^2 + 2x - x^3) dx

    2) Check where the curve meets the x-axis:

    x^3 - 2x^2 -5x +6 = 0

    Same procedure as in (1).
    Last edited by Spec; August 20th 2008 at 06:31 PM. Reason: typo in equation
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