Results 1 to 2 of 2

Math Help - sub u w/ trig?

  1. #1
    Member
    Joined
    Sep 2011
    Posts
    106
    Thanks
    1

    sub u w/ trig?

    I have been getting better but I am having trouble with this evil integral.

    Evalute the following integrel:

    \int_{}{} sin^2(3x+\frac{\pi}{8}) dx

    The answer is = \frac{x}{2}- \frac{1}{12}sin(6x+\frac{\pi}{4})+c


    Here was my first path of deduction

    \int_{}{} sin^2(3x+\frac{\pi}{8}) dx ; u=3x+\frac{\pi}{8} , u'=3

    dx in terms of u:  1dx=3du \Rightarrow du=\frac{1}{3}

    \int_{}{} sin^2(u) \frac{1}{3}du = \frac{1}{3} \int_{}{} sin^2(u)du = \frac{1}{3} \int_{}{} (sinu)^2du

    I am stuck here. I can't directly integrate anything.
    Last edited by delgeezee; December 4th 2011 at 09:07 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,835
    Thanks
    1604

    Re: sub u w/ trig?

    Quote Originally Posted by delgeezee View Post
    I have been getting better but I am having trouble with this evil integral.

    Evalute the folling integrel:

    \int_{}{} sin^2(3x+\frac{\pi}{8}) dx


    Here was my first path of deduction

    \int_{}{} sin^2(3x+\frac{\pi}{8}) dx ; u=3x+\frac{\pi}{8} , u'=3

    dx in terms of u:  1dx=3du \Rightarrow du=\frac{1}{3}

    \int_{}{} sin^2(u) \frac{1}{3}du = \frac{1}{3} \int_{}{} sin^2(u)du = \frac{1}{3} \int_{}{} (sinu)^2du

    I am stuck here. I can't directly integrate anything.
    Hint: \displaystyle \begin{align*} \sin^2{x} \equiv \frac{1}{2} - \frac{1}{2}\cos{2x} \end{align*}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Compute Trig Function Values, Solve Trig Equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 8th 2011, 08:00 PM
  2. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 08:07 AM
  3. Replies: 7
    Last Post: April 15th 2010, 09:12 PM
  4. Replies: 6
    Last Post: November 20th 2009, 05:27 PM
  5. Replies: 2
    Last Post: April 21st 2006, 04:04 PM

/mathhelpforum @mathhelpforum