Results 1 to 8 of 8

Math Help - Stuck on finding an Integral

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    87

    Stuck on finding an Integral

    Hi all,

    I am stuck on trying to find \int sin(2x+\frac{\pi}{4})cos(2x+\frac{\pi}{4})dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Have you considered \sin(2x) = 2\cdot\sin(x)\cos(x)?

    Mustn't forget one's trigonometry.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2010
    Posts
    30
    Try u substitution, with u=sin(2x+\pi/4). Then du=2cos(2x+\pi/4), and the rest is easy.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jan 2011
    Posts
    87
    Not sure how I would rewrite the expression using that Identity - something like \frac{1}{4}\int sin(2(x+\frac{\pi}{2})) dx ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2011
    Posts
    87
    Quote Originally Posted by Chaobunny View Post
    Try u substitution, with u=sin(2x+\pi/4). Then du=2cos(2x+\pi/4), and the rest is easy.
    Yea, I think that might be easier. thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Jan 2011
    Posts
    87
    Would it then be ... \frac{1}{2}\int u du = \frac{-1}{2}*\frac{u^2}{2} = \frac{-1}{4}cos(2x+\frac{\pi}{4}) ?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Unique solutions don't care how you find them. Good work, excepting the factor of 2 you missed.

    Wonderful exercise: If you do it with the trig substitution, you get the sine, but squared. Can you demonstrate that BOTH are correct?
    Hint: There's something about the solution of an indefinite integral that you probably think very little about that makes a difference.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    May 2011
    Posts
    16
    Before using the excellent hint above try using the substitution u =(2x + pi/4). It's not mandatory to make this substitution but I've always told my students to let the angle equal U, unless the angle is just x or just t, etc or if there are two angles in the integrand (like your) and they are different angles (unlike yours). This make the integral look much nicer and gives you a better chance to see that the hint above is one way to go.
    Good luck
    Steven
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the Centroid of this triangle - stuck!
    Posted in the Geometry Forum
    Replies: 4
    Last Post: August 5th 2011, 01:18 PM
  2. [SOLVED] Finding Extremal - Stuck in the middle
    Posted in the Advanced Applied Math Forum
    Replies: 5
    Last Post: November 17th 2010, 06:30 AM
  3. How does this work, finding the 3rd one?? stuck
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 17th 2010, 12:27 PM
  4. [SOLVED] stuck finding antiderivative
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 12th 2010, 01:50 PM
  5. Stuck finding area under the curve
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 2nd 2010, 09:12 AM

Search Tags


/mathhelpforum @mathhelpforum