Results 1 to 6 of 6

Math Help - Trig Substitution

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    38

    Trig Substitution

    \int \frac {1}{(x^2+a^2)^{3/2}}dx

    \int \frac {1}{(\sqrt{(x^2+a^2)})^3}dx

    x=a tan\theta
    dx=sec^2\theta

    \sqrt{(x^2+a^2)}= \sqrt{a^2tan^2\theta+a^2}= asec\theta\ ?

    \int \frac {1}{({asec\theta})^3}sec^2\theta\  ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    Looks good to me.

    We must remember that \sqrt{\sec^2\theta}=|\sec\theta|, but since \theta=\arctan\frac{x}{a}, \sec\theta is always positive.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    38
    Quote Originally Posted by Scott H View Post
    Looks good to me.

    We must remember that \sqrt{\sec^2\theta}=|\sec\theta|, but since \theta=\arctan\frac{x}{a}, \sec\theta is always positive.
    Ok thanks, I'm not sure what to do next though. u substitution? trig identities?

    \int \frac {1}{({asec\theta})^3}sec^2\theta=\
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by JJ007 View Post
    Ok thanks, I'm not sure what to do next though. u substitution? trig identities?

    \int \frac {1}{({asec\theta})^3}sec^2\theta=\


    \frac{1}{a^3} \int \cos{\theta}d\theta
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2009
    Posts
    38
    Quote Originally Posted by 11rdc11 View Post
    \frac{1}{a^3} \int \cos{\theta}d\theta
    \frac{sin{\theta\ d\theta } }{a^3}+c
    So is this the full answer to the problem or does it involve a triangle at some point?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by JJ007 View Post
    \frac{sin{\theta\ d\theta } }{a^3}+c
    So is this the full answer to the problem or does it involve a triangle at some point?
    One more step, back sub for your the trig sub

    \frac{x}{a^3\sqrt{a^2+x^2}}+C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trig substitution
    Posted in the Calculus Forum
    Replies: 15
    Last Post: June 29th 2010, 12:32 PM
  2. Trig Substitution again
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 29th 2009, 11:01 AM
  3. Trig Substitution
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 29th 2009, 03:54 AM
  4. Trig Substitution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 25th 2009, 06:11 AM
  5. Trig substitution
    Posted in the Calculus Forum
    Replies: 27
    Last Post: June 16th 2008, 06:55 PM

Search Tags


/mathhelpforum @mathhelpforum