1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Step function integral

  1. Jan 3, 2017 #1


    User Avatar
    Gold Member

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


    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

    User Avatar
    Homework Helper
    Gold Member

    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


    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

    Buzz Bloom

    User Avatar
    Gold Member

    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.

  6. Jan 3, 2017 #5


    User Avatar
    Gold Member

    Thank you for your help, everyone!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted