Results 1 to 2 of 2

Math Help - approximating definite integral using power series

  1. #1
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1

    approximating definite integral using power series

    Use a power series to approximate the definite integral to 6 decimal places:

    \int^{.5}_{0} ln (1+x^5) dx

    Need some help getting started on this and also how to evaluate it at the limits. Would I take the limit as n -> .5 somehow?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722
    Try this...
    \ln (1 + y) = \sum_{n=0}^{\infty} \frac{(-1)^n y^n}{n} so long as |y| < 1.
    So let y = x^5 to get \ln (1 + x^5) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{5n}}{n} and integrate the first few terms then sub in x=0.5.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 31st 2011, 11:47 AM
  2. Power series to approximate definite integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 24th 2011, 09:18 PM
  3. Approximating definite integral using series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 16th 2009, 03:32 PM
  4. Replies: 2
    Last Post: April 20th 2008, 08:40 PM
  5. definite integral, w/ power series.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 19th 2007, 10:13 PM

Search Tags


/mathhelpforum @mathhelpforum