Results 1 to 3 of 3

Math Help - U-Substitution problem

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    1

    U-Substitution problem

    Hi guys! I'm doing my Calc homework right now and am having a little trouble with some problems. I did one but I'm not really sure if i did it right. Could you check for me?

    ∫Sin^5(2x)Cos(2x)

    U= Sin(2x)
    Du/Dx= Cos(2x)/2
    Dx= du/2cos(2x)

    (U)^5 Cos(2x) Du/Cos(2x)/2

    So the Cos(2x) cancels and I’m left with

    (U)^5

    Now I have to do the anti derivative

    1/12U^6

    1/2Sin^6(2x)

    Is that right? If not, what did I do wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by gocubs526 View Post
    Hi guys! I'm doing my Calc homework right now and am having a little trouble with some problems. I did one but I'm not really sure if i did it right. Could you check for me?

    ∫Sin^5(2x)Cos(2x)

    U= Sin(2x)
    Du/Dx= Cos(2x)/2
    Dx= du/2cos(2x)

    (U)^5 Cos(2x) Du/Cos(2x)/2

    So the Cos(2x) cancels and Im left with

    (U)^5

    Now I have to do the anti derivative

    1/12(U^6)

    1/2Sin^6(2x) ?

    I think you mean \textcolor{red}{\frac{\sin^6(2x)}{12} + C}

    Is that right? If not, what did I do wrong?
    remember that you can always check your antiderivative by taking the derivative of your solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    151
    your answer is correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. please help with a substitution problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 2nd 2010, 12:42 PM
  2. U substitution problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 24th 2010, 06:10 PM
  3. Substitution problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 10th 2009, 03:03 PM
  4. u-substitution problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 14th 2008, 05:23 AM
  5. Need help with a u-substitution problem
    Posted in the Calculus Forum
    Replies: 12
    Last Post: September 23rd 2008, 05:09 PM

Search Tags


/mathhelpforum @mathhelpforum