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Thread: Setting up an abs. value integral

  1. #1
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    Setting up an abs. value integral

    INSTRUCTIONS
    Sketch the region enclosed by the curves and find its area:

    y= 2 +|x-1|
    y= -x/5 + 7

    I need to find the intercepts and then solve it by splitting the limits of integration between x>0 and x>0 but how do you find the intercepts?

    If this problem shows up on a test I know I won't have time or space to sketch it.
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  2. #2
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    Quote Originally Posted by HELLMACH View Post
    INSTRUCTIONS
    Sketch the region enclosed by the curves and find its area:

    y= 2 +|x-1|
    y= -x/5 + 7

    I need to find the intercepts and then solve it by splitting the limits of integration between x>0 and x>0 but how do you find the intercepts?

    If this problem shows up on a test I know I won't have time or space to sketch it.
    for x \ge 1 , 2+(x-1) = -\frac{x}{5} + 7

    for x < 1 , 2-(x-1) = -\frac{x}{5} + 7

    solve for x in both cases.


    A = \int_{-5}^1 \left(-\frac{x}{5}+7\right) - [2 - (x-1)] \, dx + \int_1^5 \left(-\frac{x}{5}+7\right) - [2 + (x-1)] \, dx<br />
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