Results 1 to 4 of 4

Thread: [SOLVED] Integral and Error Bounds

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    30

    [SOLVED] Integral and Error Bounds

    I can't quite found out how to integrate this
    (dx)/(x + x^(1/3))
    I've tried doing it by partial fraction decomposition and u-sub x^(2/3)
    Can anyone guide me to the way to solve this?

    Also, how do you find K when finding out error bounds for Midpoint/Trapezoid
    I know your suppose to find f''(x) but I don't get what you do after that
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Sep 2008
    Posts
    30
    nvm found the answers
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    $\displaystyle \int\frac{dx}{x+x^{\frac{1}{3}}}$

    Let $\displaystyle x = u^3$. Thus $\displaystyle dx=3u^2\,du$.

    Subbing in gives: $\displaystyle \int\frac{3u^2}{u^3+u}\,du$.

    Factor out the $\displaystyle 3$ and cancel out a $\displaystyle u$, which leaves: $\displaystyle 3\int\frac{u}{u^2+1}\,du$.

    Let $\displaystyle t=u^2+1$. Thus $\displaystyle dt=2u\,du$.

    Thus the integral becomes: $\displaystyle \frac{3}{2}\int\frac{dt}{t}\,dt$.

    This equals $\displaystyle \frac{3}{2}ln(t) = \frac{3}{2}ln(u^2+1)$.

    Subbing back in $\displaystyle x^{\frac{1}{3}}$ for $\displaystyle u$ gives: $\displaystyle \frac{3}{2}ln((x^{\frac{1}{3}})^2+1)$.

    Thus, $\displaystyle \int\frac{dx}{x+x^{\frac{1}{3}}} = \frac{3}{2}ln(x^{\frac{2}{3}}+1)$.


    EDIT: Oh well. Did your answer agree with mine?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2008
    Posts
    30
    yeah I got the same answer but I did it another way

    Factores a x^(1/3) from the bottom and u subbed u = x^(2/3) + 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Error Bounds for Euler's Method, finding M and L
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: Mar 13th 2011, 10:42 AM
  2. Error Bounds
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 16th 2010, 02:36 PM
  3. Taylor Polynomials error bounds
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 8th 2008, 09:46 AM
  4. Error Bounds with Trapezoid Rule
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Sep 19th 2008, 05:40 PM
  5. Error Bounds
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 10th 2007, 07:29 PM

Search Tags


/mathhelpforum @mathhelpforum