Results 1 to 5 of 5

Math Help - Indefinite Integral

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    19

    Indefinite Integral

    What is ∫(sin(√(x))/x)dx?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by th%$&873 View Post
    What is ∫(sin(√(x))/x)dx?
    This integral is unsolvable (no finite forms).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,073
    Thanks
    373
    Awards
    1
    Quote Originally Posted by th%$&873 View Post
    What is ∫(sin(√(x))/x)dx?
    The best we can do is to let u = \sqrt{x} \implies 2u~du = dx, so
    \int \frac{sin(\sqrt{x})}{x}~dx = \int \frac{sin(u)}{u^2} \cdot 2u~du = 2 \int \frac{sin(u)}{u}~du

    This integral (at least) sometimes goes by the name of "Si." (So as a function of x it is Si(x).) There is no closed-form solution to this integral.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by topsquark View Post
    This integral (at least) sometimes goes by the name of "Si."
    The \text{Si} function is defined as follows:

    {\text{Si}}\,(x) = \int_0^x {\frac{{\sin u}}<br />
{u}\,du} .

    As a definite integral, may be it could have more sense.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2007
    Posts
    19
    Thanks, everyone.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. indefinite integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 6th 2010, 09:11 PM
  2. Indefinite integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 8th 2009, 01:50 PM
  3. Indefinite integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 22nd 2008, 03:07 AM
  4. Indefinite integral?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 15th 2008, 08:36 AM
  5. Indefinite integral help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 15th 2008, 10:18 PM

Search Tags


/mathhelpforum @mathhelpforum