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Math Help - Finding the area between two functions.

  1. #1
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    Finding the area between two functions.

    Having problems with the following question.

    For the equations y=sqrt{9-x} and y=x+3
    a)Find the value of x when they intersect
    b)Find the area between the curves from x=-1 to x=2.

    -I found a to be x=0, but i am getting b wrong, weather its my arithmetic or my steps are wrong, i don't know.

    -When inputting the two functions into an integral equation, should i take them away? multiply them? or......... i have been taking them away.

    If anyone could help me with this, it would be greatly appreciated, thanks.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Finding the area between two functions.

    Quote Originally Posted by johnsy123 View Post
    -When inputting the two functions into an integral equation, should i take them away? multiply them? or......... i have been taking them away.
    A=\int_{-1}^2|\sqrt{9-x}-(x+3)|\;dx=

    \int_{-1}^0(\sqrt{9-x}-x-3)\;dx+\int_{0}^2(x+3-\sqrt{9-x})\;dx=\ldots
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  3. #3
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    Re: Finding the area between two functions.



    The area you are trying to evaluate is the combined pink and blue regions.

    For the pink region, \displaystyle y = \sqrt{9-x} is the greater function, so the area is \displaystyle \int_{-1}^0{\sqrt{9-x}\,dx} - \int_{-1}^0{x + 3\,dx}.

    For the blue region, \displaystyle y = x + 3 is the greater function, so the area is \displaystyle \int_0^2{x + 3\,dx} - \int_0^2{\sqrt{9-x}\,dx}.

    Your required area is the sum of the resulting two answers.
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