Results 1 to 6 of 6

Math Help - Integration approaches

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    5

    Integration approaches

    Hey,

    What is the best approach to integrate this:

    sqrt[ (t+a)^2 + a^2 ] dt

    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by fatlucky View Post
    Hey,

    What is the best approach to integrate this:

    sqrt[ (t+a)^2 + a^2 ] dt

    Thanks in advance
    Integrate by parts.

    u=\sqrt{(t+a)^2+a^2} and dv=1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    First let  u = t+a . The let u = a \tan x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Put  (t+a) = a\sinh{\varphi}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2011
    Posts
    5
    Damn.. I was thinking there would be a more obvious substitution I could use..
    I would not think to use these in a calculus exam :O
    Thanks for the suggestions - I'll be trying them out now and see what works best for me
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    In my opinion the best way is the simple substution x= \frac{t}{a} so that the integral becomes...

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

    ... that can be solved by parts in some steps...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A limit as x approaches a.
    Posted in the Calculus Forum
    Replies: 14
    Last Post: February 11th 2011, 04:03 AM
  2. Limit of (a^x -1)/x when x approaches 0
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 23rd 2010, 08:43 PM
  3. when x approaches to -inf in limit
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 1st 2010, 07:01 AM
  4. What is the sum as n approaches infinity?
    Posted in the Algebra Forum
    Replies: 6
    Last Post: September 7th 2009, 07:38 AM
  5. limit as h approaches 0
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 13th 2008, 09:50 AM

Search Tags


/mathhelpforum @mathhelpforum