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Math Help - Using series to evaluate integrals

  1. #1
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    Using series to evaluate integrals

    Use series to approximate the integral from 0 to 1 of...

    ((e^x)-1)/x dx

    Write out 4 terms but do not add them.

    Any help would be GREATLY appreciated....
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  2. #2
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    Quote Originally Posted by TwentyBucks View Post
    Use series to approximate the integral from 0 to 1 of...

    ((e^x)-1)/x dx

    Write out 4 terms but do not add them.

    Any help would be GREATLY appreciated....
    The integral you gave is not a good integral.
    Because the function is not defined on [0,1]
    That means we need to appeal to improper integrals.

    You can write out e^x as 4 terms:

    e^x = 1+x+x^2/2 + x^3/6

    Then,

    e^x - 1 = x+x^2/2 + x^3/6

    Thus,

    (e^x-1)/x = 1 + x/2 + x^2 / 6

    Now this is a polynomial you can integrate this easily.
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  3. #3
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    That's all I had to do? I thought I needed to find a series to represent the whole function...

    Thanks so much for the help.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by TwentyBucks View Post
    That's all I had to do? I thought I needed to find a series to represent the whole function...

    Thanks so much for the help.
    the question said to do only the first 4 terms, so there was no need to find the series to represent the "whole" function
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