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Brushing up on the basics

  1. Jan 5, 2014 #1
    I feel retarded because I'm not understanding this equation despite getting A's in all my math classes.

    [tex]i(t) = \frac{dq(t)}{dt}[/tex]

    some how becomes

    [tex]q(t) = \int^{t}_{t_{0}} i(t)dt + q(t_{0})[/tex]

    I'm guessing we apply the integral operator [tex]\int dt[/tex] to both sides. so where is the [tex]q(t_{0})[/tex] term on the RHS coming from?

    Its a charge(q) and current(i) formula as a function of time(t) if that helps make more sense.
     
    Last edited: Jan 5, 2014
  2. jcsd
  3. Jan 5, 2014 #2
    [tex]q(t) = \int^{t}_{t_{0}} i(t)dt + q(t_{0})[/tex]

    is a special case of

    [tex]f(t) = \int^{t}_{t_{0}}f'(t)dt + f(t_{0})[/tex]

    which is a corollary to the Fundamental Theorem of Calculus, sometimes referred to as the Net Change Theorem.
     
  4. Jan 6, 2014 #3

    tiny-tim

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    himatty204359! welcome to pf! :smile:
    let's rewrite that as

    [tex]q(t) - q(t_{0}) = [q(t)]^{t}_{t_{0}} = \int^{t}_{t_{0}} q'(t)dt[/tex]

    (btw, you really ought to have a different variable, eg τ, inside the ∫ :wink:)
     
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