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!

Question about integration shouldn't be too difficult

  1. Mar 4, 2009 #1
    Really, I should know the answer to this, but...

    Suppose I'm trying to perform an integration with respect to [itex]t[/itex]:

    [tex]
    \int_0^T f(\phi(t)) dt
    [/tex]

    So my function [itex]f[/itex] is explicitly a function of [itex]\phi[/itex], and [itex]\phi[/itex] depends on time [itex]t[/itex]. But then suppose I end up being able to write the integral as

    [tex]
    \int_0^T g(\phi(t)) \frac{d \phi}{dt} dt.
    [/itex]

    Can I just cancel the [itex]dt[/itex] and perform an integral with respect to [itex]\phi[/itex]? If so, I need to change the limits of integration, right?
     
  2. jcsd
  3. Mar 4, 2009 #2
    Yes, this is my understanding.

    Example: Find the mass of a rod of length L and uniform mass density D.

    M = integral of dm

    D = dm/dx

    so D dx/dm = 1 and

    M = integral of (1 dm) = integral of (D dx/dm dm) = integral of(D dx)

    Since you're now working in distance-space, you just switch the limit to the distance-space limit, namely, 0 -> L.
     
  4. Mar 4, 2009 #3
    Also known as http://en.wikipedia.org/wiki/Integration_by_substitution" [Broken].
     
    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...