Results 1 to 2 of 2

Math Help - [SOLVED] Integration by Substitution

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    10

    [SOLVED] Integration by Substitution

    I am trying to integrate the equation sin (x) * cos(cos (x)), I assume it is best done through integration by U-substitution but I cannot seem to come up with the U. Any help would be much appreciated, thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    630
    Hello, MikeDube!

    \int \sin x \cdot \cos(\cos x)\,dx

    We have: . \int\cos(\cos x)\cdot(\sin x\,dx)

    Let: u \,=\,\cos x \quad\Rightarrow\quad du \,=\,-\sin x\,dx \quad\Rightarrow\quad \sin x\,dx \,=\,-du


    Substitute: . \int \underbrace{\cos(\cos x)}_{\downarrow}\cdot\underbrace{(\sin x\,dx)}_{\downarrow}
    . . . . . . . . . . \int\; \cos u\qquad (-du)\quad=\quad - \int\cos u\,du


    Got it?

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 22nd 2010, 08:03 AM
  2. [SOLVED] Integration by substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 2nd 2010, 10:08 PM
  3. [SOLVED] Easy Integration by Substitution
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 13th 2009, 04:11 PM
  4. [SOLVED] Integration by Substitution 2
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 14th 2009, 08:22 PM
  5. [SOLVED] Integration by Substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 14th 2009, 06:27 PM

Search Tags


/mathhelpforum @mathhelpforum