Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Learning Integration with unit step function like u(x - a)

  1. Sep 11, 2005 #1
    hello maths experts
    is the following true?
    [​IMG]

    graphically, this is how i view it
    [​IMG]
     
  2. jcsd
  3. Sep 11, 2005 #2

    LeonhardEuler

    User Avatar
    Gold Member

    Yes, that's pretty much correct, but the right hand side is missing a "+C" because it is an indefinite integral.
     
  4. Sep 11, 2005 #3
  5. Sep 11, 2005 #4

    LeonhardEuler

    User Avatar
    Gold Member

    No, the integral is constant for x<a. The u(x-a) keeps the part of the integral that is dependant on x zero for x<a, so it is just the constant of integration before that. The integral should be u(x-a)[F(x)-F(a)]+C.
     
  6. Sep 11, 2005 #5
    i want to understand this graphically
    how would the graph of u(x-a)[F(x)-F(a)] look like compared to [F(x)-F(a)] ??
    am i correct to say that my bottom graph is [F(x)-F(a)] ??
     
  7. Sep 11, 2005 #6

    LeonhardEuler

    User Avatar
    Gold Member

    I am assuming you mean the bottom graph in this image, so tell me if I am wrong:
    http://img9.imageshack.us/img9/179/int28ut.jpg
    This is not the graph of [F(x)-F(a)]. The function itself is f(x)u(x-a). The area represents the integral of this, which is u(x)[F(b)-F(a)], where b is the upper limit.

    [F(x)-F(a)] represents an antiderivative of f(x) without the step function. Suppose b and c are both less than a. Obviously the integral,I, of f(x)u(x-a) from b to c is zero, but look what happens when you plug this in to the function you proposed:
    I=[F(c)-F(a)]-[F(b)-F(a)]=F(c)-F(b)
    which is not necessarily zero.
     
  8. Jun 6, 2010 #7
    We have limits between infinite to minus infinite how can i compute when i multiply a function with an unit step function. i mean i have an integral the limits of that integral is infinite to minus infinite and inside the integral i have f(t).u(t-a) this. So how can i compute this integral ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Learning Integration with unit step function like u(x - a)
Loading...