Results 1 to 3 of 3

Math Help - Part of another Trig Sub problem

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    10

    Part of another Trig Sub problem

    Solve for Y as a function of X:

     (x^2+1)^2  \frac{dy}{dx}=\sqrt{x^2+1}

    I isolate dy on one side, then take the integral of the right. After a couple of trig substitutions, I end up here but get stuck:

    y=\int \frac{1}{sec^3\theta} \\d\theta

    I think I'm on the right track. I went with a U substitution but it just didn't look right. Any help on how to finish it is greatly appreciated!
    Last edited by Got5onIt; October 30th 2007 at 10:01 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    771
    Hello, Got5onIt

    Solve: . (x^2+1)^2 \frac{dy}{dx}\;=\;\sqrt{x^2+1}

    I ended up here: . y\:=\:\int\frac{1}{\sec^3\!\theta}\,d\theta

    Did you forget the {\color{blue}dx} ?

    We have: . dy \;=\;\frac{dx}{(x^2+1)^{\frac{3}{2}}}\quad\Rightar  row\quad y \;=\;\int\frac{dx}{(x^2+1)^{\frac{3}{2}}}


    Let: x \,=\,\tan\theta\quad\Rightarrow\quad dx \,=\,\sec^2\!\theta\,d\theta

    . . And: . \sqrt{x^2+1} \:=\:\sqrt{\tan^2\!\theta+1} \:=\:\sqrt{\sec^2\!\theta} \:=\:\sec\theta


    Substitute: . \int\frac{\sec^2\!\theta\,d\theta}{\sec^3\!\theta} \;=\;\int\frac{d\theta}{\sec\theta} \;=\;\int\cos\theta\,d\theta

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    10
    Quote Originally Posted by Soroban View Post
    Hello, Got5onIt


    We have: . dy \;=\;\frac{dx}{(x^2+1)^{\frac{3}{2}}}\quad\Rightar  row\quad y \;=\;\int\frac{dx}{(x^2+1)^{\frac{3}{2}}}


    Let: x \,=\,\tan\theta\quad\Rightarrow\quad dx \,=\,\sec^2\!\theta\,d\theta

    . . And: . \sqrt{x^2+1} \:=\:\sqrt{\tan^2\!\theta+1} \:=\:\sqrt{\sec^2\!\theta} \:=\:\sec\theta


    Substitute: . \int\frac{\sec^2\!\theta\,d\theta}{\sec^3\!\theta} \;=\;\int\frac{d\theta}{\sec\theta} \;=\;\int\cos\theta\,d\theta

    I must've forgotten a sec^2 somewhere. I will go back and recheck my work. Thanks so much!!!!!!!!!!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Some trig questions part 3
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 27th 2009, 10:09 PM
  2. Some trig questions part 2
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 27th 2009, 09:53 PM
  3. Some trig questions part 1
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 27th 2009, 09:15 PM
  4. Help with solving these Trig Identities... Part 2
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 5th 2009, 06:32 AM
  5. I bet you will not know this trig question part two
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 10th 2009, 12:06 PM

Search Tags


/mathhelpforum @mathhelpforum