Results 1 to 4 of 4

Math Help - solving for a variable

  1. #1
    Newbie
    Joined
    Sep 2010
    From
    Florida
    Posts
    14

    solving for a variable

    Can the following be solved for b in terms of x?

    x=\frac{1}{4}\left(\sinh^{-1}(2b)+2b\sqrt{1+4b^2}\right)

    I post in this forum because the subject equation comes from evaluating the (arc length) integral

    x=\int_{0}^{b}\sqrt{1+4x^2}\,dx,

    and also because sinh(x) is a very calculus-y function.

    Thanks,
    Dfrtbx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Dfrtbx View Post
    Can the following be solved for b in terms of x?

    x=\frac{1}{4}\left(\sinh^{-1}(2b)+2b\sqrt{1+4b^2}\right)

    I post in this forum because the subject equation comes from evaluating the (arc length) integral

    x=\int_{0}^{b}\sqrt{1+4x^2}\,dx,

    and also because sinh(x) is a very calculus-y function.

    Thanks,
    Dfrtbx
    Please post the entire original question.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2010
    From
    Florida
    Posts
    14
    Quote Originally Posted by mr fantastic View Post
    Please post the entire original question.
    That is the entire original question. It didn't come out of a textbook, if that's what you're asking. Here's a graph of y_1=x^2 superimposed on y_2=\frac{1}{4}\left(\sinh^{-1}(2x)+2x\sqrt{1+4x^2}\right):

    http://i51.tinypic.com/avk3v7.jpg

    Gold is the former, green the latter. Essentially what I'm trying to do is find an inverse function for y_2.

    Maxima (my computer algebra system) is unable to solve the original equation x=\frac{1}{4}\left(\sinh^{-1}(2b)+2b\sqrt{1+4b^2}\right) for b in terms of x.

    EDIT: sorry... I sorta implied it in my original post, but I guess I should be more explicit. y_2=\frac{1}{4}\left(\sinh^{-1}(2x)+2x\sqrt{1+4x^2}\right) is the arc length of the function y_1=x^2 from 0 to some x.
    Last edited by Dfrtbx; October 17th 2010 at 06:27 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Dfrtbx View Post
    Can the following be solved for b in terms of x?

    x=\frac{1}{4}\left(\sinh^{-1}(2b)+2b\sqrt{1+4b^2}\right)

    [snip]
    No.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. solving for variable
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 9th 2010, 01:00 PM
  2. Replies: 2
    Last Post: August 3rd 2010, 09:08 PM
  3. Replies: 4
    Last Post: June 25th 2010, 08:37 AM
  4. solving for a variable
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 2nd 2010, 03:39 PM
  5. solving for variable
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 29th 2006, 12:46 PM

Search Tags


/mathhelpforum @mathhelpforum