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Math Help - Having trouble with finding the area between curves by integration

  1. #1
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    Having trouble with finding the area between curves by integration

    Hi,


    I'm having quite a bit of trouble with this, I understand the process of finding the area but I'm having difficulty determining the actual area I need to solve for on the graph when there are more than 2 functions. Do I find the area enclosed by all 3+ functions or all the area enclosed by all the functions?


    Thanks!
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  2. #2
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    Re: Having trouble with finding the area between curves by integration

    It depends on your problem... Which is?
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    Re: Having trouble with finding the area between curves by integration

    Usually when you graph the functions (assuming you've done it correctly), it becomes obvious what area they're talking about. So if you can give us an example, we can probably help you. Most people have difficulty setting up the integration.

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    Re: Having trouble with finding the area between curves by integration

    The question I was most recently stuck on is

    x + 2y = 0

    y = x^2

    y = x + 6
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    Re: Having trouble with finding the area between curves by integration

    First find the points where the lines cross by finding the values of x and y that satisfy any pair of equations.

    Then sketching the functions you can see which of these points are the ones you are interested in.

    Having trouble with finding the area between curves by integration-3-line-graph.png

    I suppose you are interested in the bounded area on the left side where all 3 functions form the bounds. You can discard the point on the right where the pink and grey lines cross.

    Considering the 3 points of intersection first integrate between the grey and blue functions from the first point to the second point to get the shaded area in the image below
    Having trouble with finding the area between curves by integration-3-line-graph2.png

    Then integrate between the pink and blue lines from the second point to the third point to get the shaded area in the image below
    Having trouble with finding the area between curves by integration-3-line-graph3.png
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    Re: Having trouble with finding the area between curves by integration

    Quote Originally Posted by Shakarri View Post
    First find the points where the lines cross by finding the values of x and y that satisfy any pair of equations.

    Then sketching the functions you can see which of these points are the ones you are interested in.

    ...
    Thanks for the reply. So the area you have to solve for has vertices that are the points of intersection of all of the functions?
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    Re: Having trouble with finding the area between curves by integration

    Yes that is correct
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