Results 1 to 6 of 6

Math Help - recursive integration

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    6

    recursive integration

    hey there,
    this is my first post and I am a little concerned regarding notation, but I'll do my best to be as clear as possible in asking my question.

    I am trying to find the recursive formula for evaluating the integral of In = [tangent x]^n

    The book I am studying with gives as solution this:[1/(n -1 )]*[tangent x]^(n - 1) - I(n-2).

    What I am getting, however, is something different. The way I am working is this:

    I write [tangent x]^n as [tangent x]*[tangent x]^(n - 1). I proceed finding the derivative of the second multiplier and the integral of the first and proceed with the common steps of integration in parts method.

    Now, since I get something different from what the book gives, I suspect two things. I either am rewriting the given function wrongly, and therefore I am getting a different answer, OR, the solution in the book is wrong.

    I am not looking for someone to solve this problem for me, but I would appreciate it if someone could help me clarify if I am parting the function wrongly, or perhaps the solution given in the book is wrong?

    thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7

    Re: recursive integration

    Quote Originally Posted by bibiki View Post
    I am trying to find the recursive formula for evaluating the integral of In = [tangent x]^n

    The book I am studying with gives as solution this:[1/(n -1 )]*[tangent x]^(n - 1) - I(n-2).
    Hint: write (\tan x)^n = (\sec^2x-1)(\tan x)^{n-2}. No need for integration by parts.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    6

    Re: recursive integration

    Thank you Opalg,
    I retried the assignment with your hint and it worked. Thanks again.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: recursive integration

    Quote Originally Posted by bibiki View Post
    hey there,
    this is my first post and I am a little concerned regarding notation, but I'll do my best to be as clear as possible in asking my question.

    I am trying to find the recursive formula for evaluating the integral of In = [tangent x]^n

    The book I am studying with gives as solution this:[1/(n -1 )]*[tangent x]^(n - 1) - I(n-2).

    What I am getting, however, is something different. The way I am working is this:

    I write [tangent x]^n as [tangent x]*[tangent x]^(n - 1). I proceed finding the derivative of the second multiplier and the integral of the first and proceed with the common steps of integration in parts method.

    Now, since I get something different from what the book gives, I suspect two things. I either am rewriting the given function wrongly, and therefore I am getting a different answer, OR, the solution in the book is wrong.

    I am not looking for someone to solve this problem for me, but I would appreciate it if someone could help me clarify if I am parting the function wrongly, or perhaps the solution given in the book is wrong?

    thank you!
    Hello and welcome!

    First of all, I think you should separate for cases: i) n is even. ii) n is odd.

    Second, in each case use the identity \tan^2(x)=\sec^2(x)-1 .



    EDIT:

    Seems bit strange, but I didn't saw your post Opalg, Sorry.
    Last edited by Also sprach Zarathustra; July 3rd 2011 at 02:21 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2011
    Posts
    6

    Re: recursive integration

    Zarathustra,
    thank you for your reply. I already solved the assignment. however, I don't see why would you want to separate cases for n even and odd. I know you think of positive/negative values of the function, but I don't think that matters in this case?!?!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: recursive integration

    Quote Originally Posted by bibiki View Post
    Zarathustra,
    thank you for your reply. I already solved the assignment. however, I don't see why would you want to separate cases for n even and odd. I know you think of positive/negative values of the function, but I don't think that matters in this case?!?!

    If n is even the the 'last' integral that you left to evaluate is  \int (\sec^2(x)-1)dx and if n is odd the the 'last' integral that you left to evaluate is  \int \tan(x)(\sec^2(x)-1)dx
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Look at the recursive
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 14th 2010, 05:24 AM
  2. Primitive Recursive vs Recursive Functions
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 29th 2009, 08:32 AM
  3. Recursive Integration By Parts
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 2nd 2008, 02:07 AM
  4. Replies: 9
    Last Post: September 6th 2008, 07:08 AM
  5. recursive integration formula
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 31st 2006, 12:47 AM

Search Tags


/mathhelpforum @mathhelpforum