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Maclaurin Polynomials of integrals - Help needed

  1. Oct 23, 2012 #1
    Now i'm trying to get my head around this question. I just know they're going to give us a large degree question like this in the exam...

    Let's say:

    I = ∫[e^(x^2)]dx with nodes being x=0 to x=0.5

    The 5th degree polynomial is 1 + x^2 + (1/2)(x^4)

    So my queries are:

    How would I go about finding the upper bound on the error from 0 to 0.5? - My working gives 0.012
    How do I get an approximation of I by integrating? - my working gives 0.545
    How would I get an upper bound on the integration in the previous question?

    Thanks a lot guys and girls.
     
    Last edited: Oct 23, 2012
  2. jcsd
  3. Oct 23, 2012 #2

    Mark44

    Staff: Mentor

    This is incorrect. The first few terms of the Maclaurin series for et are 1 + t + t2/2! + t3/3! + t4/4! + ...

    If you replace t by x2, what do you get?


     
  4. Oct 23, 2012 #3
    i was working under this assumption:

    P(x) = f(a) + f'(a)(x-a) + [f''(a)(x-a)^2]/2! + ....etc..

    where a=0 for Maclaurin

    hmm
     
  5. Oct 23, 2012 #4



    alright going by that i've computed which i double checked with the taylor series for a=0


    1 + x^2 + (1/2)(x^4)


    any ideas on the rest?
     
    Last edited: Oct 23, 2012
  6. Oct 23, 2012 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    So integrate! You know how to integrate that, don't you?
     
  7. Oct 23, 2012 #6
    no need to snap at me.. lol.. of course i do - look at my markings next to the bolded questions

    i just thought i could get some insight and to see if i was doing it correctly
     
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