Results 1 to 6 of 6
Like Tree2Thanks
  • 1 Post By adkinsjr
  • 1 Post By HK47

Thread: Trig Substitution

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    United States
    Posts
    72
    Thanks
    9

    Trig Substitution

    I'm trying to integrate \int \frac{\sqrt{9-x^2}}{x} \,\, dx

    I let x = 3\sin \theta \Rightarrow dx = 3\cos \theta \,\, d\theta

    made the substitution \int \frac{3\cos \theta\sqrt{9(1-\sin^2 \theta)}}{3\sin \theta} \,\, d\theta

    and simplified to 3\int \frac{\cos^2 \theta}{\sin \theta} \,\, d\theta which is where I'm stuck.

    I tried to simplify the trig functions into \cot \theta \cos \theta or \cos^2\theta \csc \theta but nothing helped
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    679
    Thanks
    19

    Re: Trig Substitution

    You can simplify like this:

    \int\frac{1-sin^2(\theta)}{sin(\theta)}d\theta=\int[{csc(\theta)-sin(\theta)] d\theta
    Last edited by adkinsjr; Jul 2nd 2013 at 12:44 PM.
    Thanks from ReneG
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    Estonia
    Posts
    24
    Thanks
    2

    Re: Trig Substitution

    Try a hyperbolic substitution x=3th(theta), it will work.
    Last edited by HK47; Jul 2nd 2013 at 01:55 PM.
    Thanks from ReneG
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2009
    Posts
    671
    Thanks
    136

    Re: Trig Substitution

    The substitution

    u^{2}=9-x^{2}

    works reasonably well.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    679
    Thanks
    19

    Re: Trig Substitution

    There are a number of ways to do it, but the way ReneG attempted it works fine as well, it was just the remaining trig that had to be worked out.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2013
    From
    Estonia
    Posts
    24
    Thanks
    2

    Re: Trig Substitution

    To: atkinsjr
    My calculus 1 class did not involve integrating csc(x), that is why I offered the simpler hyperbolic substitution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Substitution
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Mar 23rd 2013, 11:37 AM
  2. trig substitution
    Posted in the Calculus Forum
    Replies: 15
    Last Post: Jun 29th 2010, 01:32 PM
  3. Trig substitution
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 5th 2010, 06:29 AM
  4. Trig Substitution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 23rd 2010, 02:12 PM
  5. Trig substitution.. Please HELP !
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jul 30th 2009, 04:11 AM

Search Tags


/mathhelpforum @mathhelpforum