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Math Help - Finding area between two graphs

  1. #1
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    Finding area between two graphs

    Consider the area between the graphs and

    I know how to do this problem by doing it as a sum of two integrals but what I am stuck on putting it together as one function

    Alternatively this area can be computed as a single integral
    where ,



    How do I go about doing this? Thanks
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  2. #2
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    Re: Finding area between two graphs

    plot x+9=y^2 and y=11-x - Wolfram|Alpha

    As you can see, you need to split it up into two integrals.
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  3. #3
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    Re: Finding area between two graphs

    x = 11 - y

    x = y^2 - 9

    determine intersection values ...

    y^2 - 9 = 11 - y

    y^2 + y - 20 = 0

    (y + 5)(y - 4) = 0

    y = -5 , y = 4

    area = integral of (right curve - left curve) ...

    A = \int_{-5}^4 (11-y)-(y^2-9) \, dy

    finish it.
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