Unit Step Function Integral

Discussion in 'Homework Help' started by p75213, Oct 18, 2011.

  1. p75213

    Thread Starter Member

    May 24, 2011
    39
    0
    Can somebody help me with understanding how they have graphed the integral? From the integral I get the following:

    10r(t)=0, t<=0
    =10t, t>=0

    -20r(t-2)=0, t<=2
    =-20t+40, t>=2

    10r(t-4)=0, t<=4
    =10t-40. t>=4

    I can't see how the graph has been drawn from these equations???
     
  2. Zazoo

    Member

    Jul 27, 2011
    114
    43
    For t<0, the ramp functions are all zero, so:
    f(t)=0

    For 0<t<2, only the first ramp function is non-zero, so:
    f(t)=10t. (the left side of the triangle)

    For 2<t<4, both the first and second ramp function are non-zero, so:
    f(t) = (10t) + (-20t+40) = -10t +40. (the right side of triangle)

    For t>4, all three ramp functions are non-zero, so:
    f(t) = (10t) + (-20t+40) + (10t-40) = 0
     
    p75213 likes this.
  3. p75213

    Thread Starter Member

    May 24, 2011
    39
    0
    I think I need a book that explains things a bit better. Any recommendations?
     
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