Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By skeeter

Math Help - anti-derivative problem

  1. #1
    Member
    Joined
    May 2012
    From
    Toronto
    Posts
    228
    Thanks
    1

    anti-derivative problem

    I have f(x)= \frac{8}{x^3}-\frac{7}{x^7} and I want to find F(x)

    I am also given that F(1)=0

    I get F(x)= \frac{7}{6x^6}-\frac{4}{x^2}+C

    and since F(1)=0

    F(x)= \frac{7}{6*(1)^6}-\frac{4}{(1)^2}+C=0

    F(x)= \frac{7}{6}-4+C=0

    F(x)= -17/6+C=0

    so c=17/6

    however the above is wrong somewhere. I just don't see where
    Last edited by kingsolomonsgrave; November 20th 2012 at 07:45 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: anti-derivative problem

    looks fine to me ...

    F(x) = \frac{7}{6x^6} - \frac{4}{x^2} + \frac{17}{6}

    F(1) = \frac{7}{6} - \frac{24}{6} + \frac{17}{6} = 0

    F'(x) = \frac{8}{x^3} - \frac{7}{x^7}
    Thanks from kingsolomonsgrave
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2012
    From
    Toronto
    Posts
    228
    Thanks
    1

    Re: anti-derivative problem

    hmmm, thanks! i was entering the answer into an online test, so it could be something i entered wrong (typo) or the online system has a bug.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2012
    From
    San Diego, California
    Posts
    1

    Re: anti-derivative problem

    Hi-

    I Thought some might benefit from seeing all the steps to this problem:

    Given:

    f ' (x) = 8 / x^3 - 7 / x^7 Where f(1)=0

    Rewrite:

    f ' (x) = 8*x^(-3) - 7*x^(-7)

    Integrate:

    8*x^(-3+1) 7*x^(-7+1)
    = ∫ -------------- - ---------------
    (-3+1) (-7+1)

    = 8*x^(-2)/(-2) - 7*x^(-6)/(-6)

    = -4*x^(-2) + (7/6)*x^(-6) + C

    Answer:

    f (x) = -4 / x^2 + 7 / 6*x^6 + C

    At f (1) = 0

    f (1) = -4 / (1)^2 + 7 / 6*(1)^6 + C = 0

    = -4 + 7/6 + C = 0

    Common Denominator:

    = -24 / 6 + 7 / 6 + C = 0

    = -17 / 6 + C = 0

    C = 17 / 6

    Answer:

    f (x) = -4 / x^2 + 7 / 6*x^6 + 17 / 6
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,964
    Thanks
    1008

    Re: anti-derivative problem

    OP - please write down here EXACTLY how you entered this into your online test. Chances are you have a syntax error somewhere.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to do this Anti derivative problem.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 9th 2009, 06:17 AM
  2. Anti-Derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 16th 2009, 04:30 PM
  3. Help with Anti-derivative problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 19th 2008, 03:09 AM
  4. Anti derivative problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 1st 2007, 02:44 PM
  5. Anti-derivative problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2007, 02:48 PM

Search Tags


/mathhelpforum @mathhelpforum