Results 1 to 2 of 2

Math Help - [SOLVED] Trig Integrals

  1. #1
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1

    [SOLVED] Trig Integrals

    Hey everyone!

    Integrate.

    \int 59   cos^2 x \cdot sin (2x) dx


    Here is what I have done so far:

    59 \int (\frac{1}{2}(1 + cos 2x) \cdot (2 sinx cosx) dx

    Are those the correct identities to substitute in there?

    Also need some help to go on to the next step of this.

    Thanks y'all!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,659
    Thanks
    600
    Hello, mollymcf2009!

    Integrate: . 59\int \cos^2\!x\sin2x\, dx


    Here is what I have done so far: . 59 \int \left(\frac{1 + \cos 2x}{2}\right)(2\sin x\cos x)\,dx
    Don't change both of them.
    There are a few ways to approach this problem.
    Here's one of them . . .

    We have: . 59\int\cos^2\!x(2\sin x\cos x)\,dx \;=\;118\int\cos^3\!x(\sin x\,dx)

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

    Substitute: . 118\int u^3(-du) \;\;=\;\;-118\int u^3\,du \;\;=\;\;-118\,\frac{u^4}{4} + C \;\;=\;\;-\frac{59}{2}u^4 + C

    Back-substitute: . -\frac{59}{2}\cos^4\!x + C

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trig integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 8th 2009, 10:22 PM
  2. Trig integrals
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 2nd 2009, 09:01 AM
  3. Trig integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 16th 2009, 06:45 PM
  4. Trig integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 15th 2009, 05:53 AM
  5. Trig Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 30th 2008, 03:58 PM

Search Tags


/mathhelpforum @mathhelpforum