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

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


    User Avatar
    Science Advisor
    Homework Helper

    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:)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook