Results 1 to 2 of 2

Math Help - Something to do with Reduction Formulae...?

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    6

    Something to do with Reduction Formulae...?

    Hello everybody,

    I have got into a terrible mess with a question.

    In my question, I am asked to derive the reduction formulae for integrating (sin x)^m * (cos x)^n, which are on the bottom of this webpage:

    Reduction Formulas

    I keep nearly getting there, but not quite near enough! I think I must be doing the reduction part wrong.

    Any help would be greatly appreciated!!

    Jessica.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by j_clough View Post
    Hello everybody,

    I have got into a terrible mess with a question.

    In my question, I am asked to derive the reduction formulae for integrating (sin x)^m * (cos x)^n, which are on the bottom of this webpage:

    Reduction Formulas

    I keep nearly getting there, but not quite near enough! I think I must be doing the reduction part wrong.

    Any help would be greatly appreciated!!

    Jessica.
    Hello,

    What exactly did you do ?


    integrate by parts with u=cos^(n-1) (x) and v'=cos(x)*sin^m (x)


    this gives :
    I_{m,n}=\frac{\cos^{n-1}(x) \sin^{m+1}(x)}{m+1}+\frac{n-1}{m+1} \int \left(\sin(x) \cos^{n-2}(x)\right)*\left(\sin^{m+1}(x)\right) ~ dx

    I_{m,n}=\frac{\cos^{n-1}(x) \sin^{m+1}(x)}{m+1}+\frac{n-1}{m+1} \int \cos^{n-2}(x) \sin^m (x) \sin^2(x) ~ dx

    Use the identity \sin^2(x)=1-\cos^2(x) to find I_{m,n-2} and I_{m,n} in the right hand side of the equation =)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Reduction Formulae Help!
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 3rd 2009, 08:25 AM
  2. Reduction formulae.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 10th 2008, 01:42 AM
  3. Reduction formulae......again.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 4th 2008, 03:26 AM
  4. Reduction Formulae
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 3rd 2008, 10:31 PM
  5. Reduction formulae help!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 7th 2008, 04:18 AM

Search Tags


/mathhelpforum @mathhelpforum