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!

Homework Help: Integral from expansion

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data

    f(x) = x^4 - 3x^3 + 9x^2 +22x +6 in powers of (x-2)

    Hence evaluate integral,
    (limits 2.2 - 2) f(x) dx

    2. Relevant equations

    Taylor expansion for the first part
    integral f(x) dx with limits 2.2-2

    3. The attempt at a solution

    Expansion of the function I've done comes to
    78 +46(x-2) +18(x-2)^2 +9/2(x-2)^3 +3/4(x-2)^4

    But then I don't know how the x-2 relates to the limits 2.2 - 2,
    do I integrate the original integral or the expanded one? And then how do I use the integral to get the exact value

    any help appreciated
  2. jcsd
  3. Apr 5, 2014 #2


    User Avatar
    Homework Helper

    The function is a fourth-order polynomial. Expansion in powers of [itex]u = x - 2[/itex] is nothing more than substituting [itex]x = u + 2[/itex] and collecting powers of [itex]u[/itex].

    Start with [itex]\int_2^{2.2} f(x)\,dx[/itex] and consider the substitution [itex]x = u + 2[/itex].
  4. Apr 5, 2014 #3


    User Avatar
    Science Advisor

    Yes, but finding the Taylor series expansion about x= 2, as chemphys1 does, is a good way of doing that.

    Exactly right!
  5. Apr 5, 2014 #4
    Have I got this right,

    I integrate f(x) but with x = u-2

    i.e integral of (u-2)^4 - 3(u-2)^3 etc

    with the new limits being 0.2 - 0?

    Not really sure what the point of the expansion I did was?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted