1. Not finding help here? Sign up for a free 30min 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!

Change of Variables

  1. Apr 6, 2015 #1
    1. The problem statement, all variables and given/known data
    In the book it gave the example for standard change of variables as,
    z = x / 1 + x or equivalently x = z / 1 - z , then

    dx = dz / (1 - z)^2 , thus (2)

    1 / (1 - z)^2 f (z / 1 - z) dz (3)

    This is what I am trying to accomplish but with the expression x^3 / (e^x - 1) dx. So I can put this expression equal to z and find equivalent equal to x then find dx eq(2) then final result eq (3).

    2. Relevant equations
    integral of f(x) dx

    3. The attempt at a solution
    I found the derivative to be (3*x^2/(e^x - 1)) - (x^3 * e^x / (e^x - 1)^2) but not getting the final result like in equation (3) from above maybe I am doing change of variables wrong. I have seen the formulas with variables online but still not getting it. If someone could help that would be GREAT!
     
  2. jcsd
  3. Apr 7, 2015 #2

    BiGyElLoWhAt

    User Avatar
    Gold Member

    Sorry you're just now getting a response. Welcome to PF!
    they used the chain rule for the derivative
    You start out with ##\int F(x)dx## and make the substiution ##x =\frac{z}{1-z}## and obtain ##\int F(\text{substitute here})dx## you also need to substitute dx for (some stuff)*dz. That (some stuff) is the differential of the substitution, or in other words ##\frac{dx}{dz}##
     
  4. Apr 7, 2015 #3

    Mark44

    Staff: Mentor

    I'm positive that what you wrote is not what you meant.
    You have ##z = \frac x 1 + x## and ##x = \frac z 1 - z##.

    Since that's not what you intended, use parentheses around the denominators, like so:
    z = x/(1 + x), and x = z/(1 - z).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Change of Variables
  1. Change of Variables (Replies: 0)

  2. Change of Variables (Replies: 4)

  3. Change in variables (Replies: 7)

  4. Change of variable (Replies: 5)

  5. Change of Variables (Replies: 1)

Loading...