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Step function integral

  1. Jan 3, 2017 #1

    Rectifier

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    Gold Member

    The problem
    I want to calculate ## \int^6_{-6} \frac{g(x)}{2+g(x)} \ dx ## for the step function below.


    2YSK7nM.jpg


    The attempt
    I started with rewriting the function as with the help of long-division
    ## \int^6_{-6} \frac{g(x)}{2+g(x)} \ dx = \int^6_{-6} 1 \ dx - 2\int^6_{-6} \frac{1}{g(x)+2} \ dx##

    I know that ##\int^6_{-6} 1 \ dx = 12## but thats about it. I am not sure how I should continue.

    And here is where I get stuck.
     
    Last edited: Jan 3, 2017
  2. jcsd
  3. Jan 3, 2017 #2

    Charles Link

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    Homework Helper

    If you look closely at ## g(x) ##, it takes on constant values for various intervals. You need to break up the integral from -6 to 6 into these various segments.
     
  4. Jan 3, 2017 #3

    Mark44

    Staff: Mentor

    This shouldn't be too difficult. On the interval [-6, -4], g(x) = -1, so g(x) + 2 = 1. What is ##\int_{-6}^{-4} \frac 1 1 dx##? Do the same for the other intervals.
     
  5. Jan 3, 2017 #4
    Hi Rectifier:

    I suggest breaking the integral into six pieces, one piece for each step. For each piece, g(x) has a specific constant value, so the integrand is a specific constant.

    Hope this helps.

    Regards,
    Buzz
     
  6. Jan 3, 2017 #5

    Rectifier

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    Gold Member

    Thank you for your help, everyone!
     
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