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Math Help - Area between curves (with an absolute value AHHH)

  1. #1
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    Area between curves (with an absolute value AHHH)

    Absolute values throw me off. Can anyone break it down for me please?

    Find the area of the region between the curves y = |x| and y = x^2 - 2

    I start off finding the points of intersection which would be:

    |x| = x^2 - 2

    right? What now though? Thanks a bunch!
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  2. #2
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    The next step is to solve these (separately):

    x = x^2-2
    and
    -x = x^2-2

    then you have to discard any solutions with x<0 for the first one and discard the solutions with -x<0 for the 2nd. Then see how you go
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  3. #3
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    Hello, kep84!

    Find the area of the region between the curves y \:= \:|x| and y \:= \:x^2 - 2
    Did you make a sketch?
    Code:
         (-2,2)         |         (2,2)
            *           |           *
            ::*         |         *::
             :::*       |       *:::
             *::::*     |     *::::*
              ::::::*   |   *::::::
              *:::::::* | *:::::::*
          -----*:-:-:-:-*-:-:-:-:*-----
                 *::::::|::::::*
                    *:::|:::*
                        *
                        |

    Can you finish it now?

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  4. #4
    MHF Contributor kalagota's Avatar
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    another hint is to solve the area on left of the y-axis and on the right separately, then add them together..
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