Results 1 to 3 of 3

Math Help - Intigrating this seemingly simple expression

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    2

    Intigrating this seemingly simple expression

    I know that the antiderivative is cos^2(x) is (x+cos(x)sin(x))/2, but how the heck can you derive it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jagged View Post
    I know that the antiderivative is cos^2(x) is (x+cos(x)sin(x))/2, but how the heck can you derive it?
    Make the appropriate substitution suggested by the double angle formula:

    \cos (2x) = 2 \cos^2 (x) - 1 \Rightarrow \cos^2 (x) = \frac{1}{2} \, (\cos(2x) + 1).

    Then, after integrating, make the substitution \sin (2x) = 2 \sin x \cos x in your answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    2
    thanks... ive forgotten basic methods of integration since spring break
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A seemingly simple proof
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: July 8th 2010, 10:09 PM
  2. seemingly simple derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 17th 2009, 07:05 PM
  3. Help with a (seemingly?) simple proof.
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: May 27th 2009, 10:38 PM
  4. Trouble with a seemingly simple integral!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 26th 2009, 03:08 AM
  5. Another seemingly simple integral
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 25th 2009, 02:44 PM

Search Tags


/mathhelpforum @mathhelpforum