Results 1 to 5 of 5

Math Help - Integrating a fraction/square roots when 'x' is on the bottom

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    7

    Integrating a fraction/square roots when 'x' is on the bottom

    How would I transpose this formula so I can integrate it? I'm not good with integrating fractions or square roots.

    Integrate:

    Q1) \frac{dy}{dx}= \frac{x^3-2x}{x}

    Q2) (\sqrt{x}+1)^2

    It's the fractions and square roots that are annoying. For the square root, I know I'd have to write two brackets out and possibly expand, but don't know how I would expand with a square root - So does the 'x' in the square root become: x^\frac{1}{2}? Or something along those lines..

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2009
    Posts
    290
    Am I reading this right?

    \frac{x^3-2x}{x}

    If that's right, just divide it, then it becomes x^2-2

    That's easy to integrate.

    For Q2, just expand it, and you'll get x+2\sqrt x+1 Integrating that is just \frac {1}{2} x^2+\frac {4}{3} x\sqrt x+x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    7
    Quote Originally Posted by chengbin View Post
    Am I reading this right?

    \frac{x^3-2x}{x}

    If that's right, just divide it, then it becomes x^2-2

    That's easy to integrate.

    For Q2, just expand it, and you'll get x+2\sqrt x+1 Integrating that is just \frac {1}{2} x^2+\frac {4}{3} x\sqrt x+x
    Oh ok, yep Q1 is easy to Integrate..

    Just quickly, for Q2, where did you get the 4 over 3 from? and if you integrated 'x' by itself, wouldn't you get \frac{x^2}{2}?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2009
    Posts
    290
    \int 2\sqrt x = \int 2x^\frac {1}{2}

    \frac{2}{\frac{3}{2}}x^\frac {3}{2}

    \frac {4}{3} x^\frac {3}{2} = \frac {4}{3} x(x^\frac {1}{2}) = \frac {4}{3}x\sqrt x
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2009
    Posts
    7
    Ohh yip, thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrating a fraction
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 1st 2011, 03:29 AM
  2. Replies: 1
    Last Post: May 2nd 2010, 02:45 PM
  3. Integrating Square Roots
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 2nd 2010, 02:41 PM
  4. integrating a fraction of u
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 3rd 2009, 11:06 PM
  5. Integration with a square root at the bottom
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2008, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum