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Integral from expansion

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

    expand
    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

    pasmith

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    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

    HallsofIvy

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    Staff Emeritus
    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?
     
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