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Math Help - area using integrals

  1. #1
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    area using integrals

    Hi, the problem starts out by giving:
    y = 2+|x-1| and y = -(1/5)x+7

    the next step in the solution book takes y = 2+|x-1| and turns it into:
    3-x, x<= 1
    1+x, x >=1

    I know that 3-x is negative and 1+x is positive but how do you figure that out?
    Thank you
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  2. #2
    Eater of Worlds
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    What are you to do exactly. Are you given limits of integration?.

    Break the abs up into two separate integrals.

    \int_{\frac{-15}{2}}^{1}[(\frac{-1}{5}x+7)-(-x+1)]dx+\int_{1}^{\frac{10}{3}}[(\frac{-1}{5}x+7)-(x+3)]dx

    EDIT: Oops, looks like I mistakenly used 2+|x+1| instead of 2+|x-1|. You get the idea. Adjust accordingly.
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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