Results 1 to 2 of 2

Math Help - Integration with trigonometry

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    43

    Integration with trigonometry

    Hi,

    Can someone please show me how to solve this, step by step?

    Integrate the following: sinxcosxcos2x

    Apparently the answer is 1/8(sin2x)^2 + C

    Does sinxcosx go outside of the integrand as a factor?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,591
    Thanks
    1445
    Quote Originally Posted by CSG18 View Post
    Hi,

    Can someone please show me how to solve this, step by step?

    Integrate the following: sinxcosxcos2x

    Apparently the answer is 1/8(sin2x)^2 + C

    Does sinxcosx go outside of the integrand as a factor?
    These sorts of problems are easiest if you can use trigonometric identities to simplify the integrand.

    Remember that \sin{2X} = 2\sin{X}\cos{X},

    \cos{2X} = \cos^2{X} - \sin^2{X}

    and \sin^2{x} + \cos^2{x} = 1.



    That means

    \sin{x}\cos{x}\cos{2x} = \frac{1}{2}\sin{2x}\cos{2x}

     = \frac{1}{4}\sin{4x}.


    Therefore:

    \int{\sin{x}\cos{x}\cos{2x}\,dx} = \int{\frac{1}{4}\sin{4x}\,dx}

     = -\frac{1}{16}\cos{4x} + c

     = -\frac{1}{16}(\cos^2{2x} - \sin^2{2x}) + c

     = -\frac{1}{16}(1 - \sin^2{2x} - \sin^2{2x}) + c

     = -\frac{1}{16}(1 - 2\sin^2{2x}) + c

     = -\frac{1}{16} + \frac{1}{8}\sin^2{2x} + c

     = \frac{1}{8}\sin^2{2x} + C, where C = c - \frac{1}{16}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration with trigonometry
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 1st 2010, 07:32 AM
  2. Integration problem with trigonometry
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 3rd 2010, 08:34 PM
  3. integration of inverse trigonometry
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 4th 2009, 02:58 AM
  4. Replies: 1
    Last Post: September 25th 2009, 07:24 AM
  5. Trigonometry Integration
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 1st 2007, 10:14 AM

Search Tags


/mathhelpforum @mathhelpforum