Results 1 to 4 of 4

Math Help - Integrating the second derivative

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    36

    Integrating the second derivative

    given f''(x) = -25sin(5x) and f'(0) = 3 and f(0) = -2, find f(pi/6)

    I am trying to figure out how to integrate the second derivative into the first derivative and make it 3, then integrate into a function of 0 that equals -2.

    How do I integrate the second derivative into the first derivative?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,969
    Thanks
    1011
    Quote Originally Posted by derekjonathon View Post
    given f''(x) = -25sin(5x) and f'(0) = 3 and f(0) = -2, find f(pi/6)

    I am trying to figure out how to integrate the second derivative into the first derivative and make it 3, then integrate into a function of 0 that equals -2.

    How do I integrate the second derivative into the first derivative?
    f''(x) = -25\sin{(5x)}

    f'(x) = \int{-25\sin{(5x)}\,dx}

    f'(x) = 5\cos{(5x)} + C.


    You know that f'(0) = 3, so

    3 = 5\cos{(5\cdot 0)} + C

    3 = 5 + C

    C = -2.


    So f'(x) = 5\cos{(5x)} - 2

    f(x) = \int{5\cos{(5x)} - 2\,dx}

    f(x) = \sin{(5x)} - 2x + C.


    You know that f(0) = -2, so

    -2 = \sin{(5\cdot 0)} - 2\cdot 0 + C

    C = -2.


    Therefore

    f(x) = \sin{(5x)} - 2x - 2.


    Now find f\left(\frac{\pi}{6}\right).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    36

    Thanks!

    It seems easy when you explain it that way!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    "All truths are easy to understand once they are discovered; the point is to discover them." - Galileo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. integrating factor proof/ partial derivative wrt xy
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 4th 2010, 05:57 AM
  2. need help on integrating this
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 4th 2010, 06:29 AM
  3. integrating
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 5th 2010, 07:51 PM
  4. need help integrating (e^(x^2)-2x) / (e^x^2)dx
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 25th 2009, 03:32 PM
  5. integrating
    Posted in the Calculus Forum
    Replies: 12
    Last Post: May 30th 2007, 12:26 PM

Search Tags


/mathhelpforum @mathhelpforum