Results 1 to 5 of 5

Math Help - rationalizing substitution

  1. #1
    Member
    Joined
    Nov 2005
    Posts
    172

    rationalizing substitution

    evalute \int_{0}^{1} \dfrac{\sqrt{t}}{t+1}dt

    u = \sqrt{t}, u^2 = t, 2udu = dt

    need help setting this up:
     \int \frac{u*2udu}{u^2+1}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2005
    Posts
    172
    i think i got the answer:  2\sqrt{1} -2arctan(\sqrt{1}) - 2\sqrt{0}-2arctan(\sqrt{0})
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by viet View Post
    evalute \int_{0}^{1} \dfrac{\sqrt{t}}{t+1}dt

    u = \sqrt{t}, u^2 = t, 2udu = dt

    need help setting this up:
     \int \frac{u*2udu}{u^2+1}
    \frac{\sqrt{x}}{x+1} = \frac{x}{\sqrt{x} (x+1)} = \frac{2x}{\boxed{2\sqrt{x}} (x+1)}

    The thing in the box is the derivative, that is why I wrote it like that if I use the substitution:
    t = \sqrt{x} \Rightarrow t' = \frac{1}{2\sqrt{x}}

    That means,
    \int_0^1 \frac{t^2}{t^2+1} dt

    Can you do if frum heir?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2005
    Posts
    172
    yea thanks
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2007
    Posts
    237

    This is the substitution

    Quote Originally Posted by viet View Post
    evalute \int_{0}^{1} \dfrac{\sqrt{t}}{t+1}dt

    u = \sqrt{t}, u^2 = t, 2udu = dt

    need help setting this up:
     \int \frac{u*2udu}{u^2+1}
    This is the substitution:
    Attached Thumbnails Attached Thumbnails rationalizing substitution-19june2007.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rationalizing
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 14th 2011, 07:01 AM
  2. Rationalizing the Denominator
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 23rd 2009, 10:43 PM
  3. Help with rationalizing expressions
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 3rd 2008, 10:21 AM
  4. Rationalizing the Denominator #2
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 10th 2008, 01:57 PM
  5. Rationalizing
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 16th 2007, 09:17 PM

Search Tags


/mathhelpforum @mathhelpforum