Results 1 to 3 of 3

Math Help - [SOLVED] Arc length integral

  1. #1
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,663
    Thanks
    298
    Awards
    1

    [SOLVED] Arc length integral

    Hey, I derived an integral for a student, but can't find a way to integrate it.

    \int \sqrt{1 + \left ( \frac{3x^2}{4} - \frac{1}{3x^2} \right )^2}~dx

    My calculator gives
    \frac{3x^4 - 4}{12x} + C

    Any ideas how to do it?

    Thanks.
    -Dan
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    \int {\sqrt {1 + \frac{{9x^4 }}<br />
{{16}} - \frac{1}<br />
{2} + \frac{1}<br />
{{9x^4 }}} \,dx}  = \int {\sqrt {\frac{{9x^4 }}<br />
{{16}} + \frac{1}<br />
{2} + \frac{1}<br />
{{9x^4 }}} }\,dx  = \int {\left( {\frac{{3x^2 }}<br />
{4} + \frac{1}<br />
{{3x^2 }}} \right)\,dx} .

    And we're done.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,663
    Thanks
    298
    Awards
    1
    Quote Originally Posted by Krizalid View Post
    \int {\sqrt {1 + \frac{{9x^4 }}<br />
{{16}} - \frac{1}<br />
{2} + \frac{1}<br />
{{9x^4 }}} \,dx}  = \int {\sqrt {\frac{{9x^4 }}<br />
{{16}} + \frac{1}<br />
{2} + \frac{1}<br />
{{9x^4 }}} }\,dx  = \int {\left( {\frac{{3x^2 }}<br />
{4} + \frac{1}<br />
{{3x^2 }}} \right)\,dx} .

    And we're done.
    Oh dear God.

    It was right in front of me the whole time.

    Thanks!

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Length of Arc - Integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 28th 2010, 07:41 PM
  2. [SOLVED] Length of a curve
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 14th 2010, 11:07 AM
  3. [SOLVED] Arc Length help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 22nd 2009, 04:28 PM
  4. [SOLVED] Finding Arc length
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 24th 2008, 05:51 PM
  5. [SOLVED] Question regarding length
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 19th 2008, 10:32 AM

Search Tags


/mathhelpforum @mathhelpforum