Results 1 to 5 of 5

Math Help - How do I finish this evaluation of reduction formula?

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    157

    How do I finish this evaluation of reduction formula?

    I wanted to find a reduction formula for \int_0^{\pi/4} tan^n x dx

    And I found this as I_{n} = \frac{1}{n-1} - I_{n-2}

    I found I_1 as \frac{ln2}{2} and the last thing I want to do is find, for example, I_5.

    My working here is as follows:

    I_5 = \frac{1}{4} \int_0^{\pi/4} tan^3 x dx
    I_3 = \frac{1}{2} \int_0^{\pi/4} tan x dx

    Which gave me

    I_5 = \frac{ln2}{8} - \frac{1}{8}

    Now I think that's wrong. I know I'm looking for an answer in the form

    a\ln2 - b where a and b are fractions, but I know my answer's wrong because it is negative - and I checked on wolfram alpha which gives a different integral. Could you please tell me what I have done wrong? Thanks if you can help me
    Last edited by db5vry; March 5th 2010 at 07:20 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    it's actually I_{n}=\frac{1}{n-1}-I_{n-2}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    157
    Quote Originally Posted by Krizalid View Post
    it's actually I_{n}=\frac{1}{n-1}-I_{n-2}.
    That was a typo there sorry! I've edited it now. By the way, everything I have done in the rest of the question was based on it being 2 rather than 1 - I know that the ln2/2 part is correct, I know it's after that where my answer falls apart.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    I_5  = \frac{1}<br />
{4} - I_3  = \frac{1}<br />
{4} - \left[ {\frac{1}<br />
{2} - I_1 } \right] =  - \frac{1}<br />
{2} + I_1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2008
    Posts
    157
    Quote Originally Posted by Plato View Post
    I_5  = \frac{1}<br />
{4} - I_3  = \frac{1}<br />
{4} - \left[ {\frac{1}<br />
{2} - I_1 } \right] =  - \frac{1}<br />
{2} + I_1
    I am an idiot. I've just figured out what I've done. I had what you gave as the last stage, but instead of adding and subtracting the terms, I've inexplicably multiplied it all out.

    Everyone thanks very much for your time
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using a Reduction Formula
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 7th 2009, 12:43 PM
  2. Reduction formula
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 26th 2009, 02:26 AM
  3. need help with reduction formula
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 24th 2009, 09:01 PM
  4. reduction formula.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 10th 2009, 03:23 AM
  5. Reduction Formula
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2008, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum